FABER POLYNOMIAL COEFFICIENTS FOR GENERALIZED BI SUBORDINATE FUNCTIONS OF COMPLEX ORDER
|
|
- Vernon Phillips
- 5 years ago
- Views:
Transcription
1 Journal of Mathematical Inequalities Volume, Number 3 (08), doi:0.753/jmi FABER POLYNOMIAL COEFFICIENTS FOR GENERALIZED BI SUBORDINATE FUNCTIONS OF COMPLEX ORDER ERHAN DENIZ, JAY M. JAHANGIRI, SAMANEH G. HAMIDI AND SIBEL K. KINA (Communicated by J. Pečarić) Abstract. In this paper, we obtain the upper bounds for the n-th (n 3) coefficients for generalized bi-subordinate functions of complex order by using Faber polynomial expansions. The results, which are presented in this paper, would generalize those in related works of several earlier authors.. Introduction Let A be the class of analytic functions in the open unit disk D = z C : z < } let S be the class of function f that are univalent in D are of the form f = z k= a k z k. A function f A is said to be subordinate to a function g A, denoted by f g, if there exists a function w A with w(0) = 0 w < satisfying f = g(w). We let S consist of starlike functions f A, that is Rez f f > 0 in D C consist of convex functions f A, that is Rez f f > 0 in D. In terms of subordination, these conditions are, respectively, equivalent to S f A : z f f z } z C f A : z f f z }. z A generalization of the above two classes, according to Ma Minda [0], are S z f } (ϕ) f A : f ϕ Mathematics subject classification (00): Primary 30C45, Secondary 30C80. Keywords phrases: Fabel polynomials, analytic, subordinate, convex, starlike, bi-univalent functions. c Ð, Zagreb Paper JMI
2 646 E. DENIZ, J. M. JAHANGIRI, S. G. HAMIDI AND S. K. KINA C(ϕ) f A : z f } f ϕ where ϕ is a positive real part function normalized by ϕ(0) =, ϕ (0) > 0 ϕ maps D onto a region starlike with respect to symmetric with respect to the real axis. Obvious extensions of the above two classes (see []) are S (γ;ϕ) f A : ( z f ) } γ f ϕ; γ C \ 0} C (γ;ϕ) f A : ( z f ) } γ f ϕ; γ C \ 0}. In literature, the functions belonging to these classes are called Ma-Minda starlike convex of complex order γ (γ C 0}), respectively. Some of the special cases of the above two classes S (γ;ϕ) C(γ;ϕ) are () S (,(Az) (Bz))= S [A,B] C (,(Az) (Bz))=C[A,B], ( B < A ) are classes of Janowski starlike convex functions, respectively, () S (( β)e iδ cosδ,(z) ( z))= S [δ,β] C(( β)e iδ cosδ, (z) ( z)) = C[δ,β], ( δ < π, 0 β < ) are classes of δ -spirallike δ -Robertson univalent functions of order β, respectively, (3) S (,(( β)z) ( z)) = S (β) C (,(( β)z)) ( z)) = C(β) (0 β < ) are classes of starlike convex functions of order β, respectively, ) β ) = S β C ( (4) S (, ( z z, ( z z convex functions of order β, respectively, (5) S (, z ) = SL = f A : ) β ) = C β are class of strongly starlike ( z f f ) < } is class of lemniscate starlike functions, (6) S (γ,(z) ( z))=s [γ] C(γ,(z) ( z))=c[γ] (γ C 0}) are classes of starlike convex functions of complex order, ) respectively, (7) S (,q k ) = k SP = f A : Re > k is class of ( z f f } z f f k-parabolik starlike functions, ( ) } (8) C (,q k ) = k U CV = f A : Re z f f > k z f f is class of k-uniformly convex functions. Here, for 0 k< the function q k : D w=uiv C : u > k ( (u ) v ), u > 0} has the form q k = Q zq z..., (z D) where B ; 0 k <, k 8 Q = ; k =, π π 4(k ) t(t)k (t) ; k >,, Q = (B ) 3 Q ; 0 k <, 3 Q ; k =, [4K (t)(t 6t) π ] 4 t(t)k (t) Q ; k >, (.)
3 FABER POLYNOMIAL COEFFICIENTS FOR GENERALIZED BI-SUBORDINATE FUNCTIONS 647 with B = π arccosk K (t) is the complete elliptic integral of first kind (see [8]). A function f A is said to be bi-univalent in D if both f its inverse map f are univalent in D. Let σ be the class of functions f S that are bi-univalent in D. For a brief history interesting examples of functions which are in (or are not in) the class σ, including various properties of such functions we refer the reader to the work of Srivastava et al. [] references therein. Bounds for the first few coefficients of various subclasses of bi-univalent functions were obtained by a variety of authors including ([4, 5, 6, 7], [0], [9], [3, 4, 5, 6, 7]). Not much was known about the bounds of the general coefficients a n ;n 4 of subclasses of σ up until the publication of the article [4] by Jahangiri Hamidi followed by a number of related publications (see [] [7]). In this paper, we apply the Faber polynomial expansions to certain subclasses of bi-univalent functions obtain bounds for their n th;(n 3) coefficients subject to a given gap series condition.. Coefficient estimates In the sequel, it is assumed that ϕ is an analytic function with positive real part in the unit disk D, satisfying ϕ(0) =, ϕ (0) > 0, ϕ(d) is symmetric with respect to the real axis. Such a function is known to be typically real with the series expansion ϕ = z B z B 3 z 3... > 0. Motivated by a class of functions defined by the first author [7], we define the following comprehensive class of analytic functions S (λ,γ;ϕ) f A : γ ( z f λ z f ) ( λ) fλ z f ϕ; 0 λ, γ C \ 0} }. A function f A is said the be generalized bi-subordinate of complex order γ type λ if both f its inverse map g = f are in S (λ,γ;ϕ). As special cases of the class S (λ,γ;ϕ) we have S (0,γ;ϕ) S (γ;ϕ) S (,γ;ϕ) C (γ;ϕ). In the following theorem we use the Faber polynomials introduced by Faber [9] to obtain a bound for the general coefficients of the bi-univalent functions in S (λ, γ; ϕ) subject to a gap series condition. THEOREM.. Let 0 λ γ C 0}. If both functions f = z n= ρ nz n its inverse map g = f are in S (λ,γ;ϕ) ρ m = 0; m n then γ ρ n (n )(λ(n )). Proof. If we write Λ( f) = λ z f ( λ) f then f S (λ,γ;ϕ) ( zλ ) ( f) γ Λ( f) ϕ
4 648 E. DENIZ, J. M. JAHANGIRI, S. G. HAMIDI AND S. K. KINA g = f S (λ,γ;ϕ) γ ( wλ ) (g(w)) Λ(g(w)) ϕ(w). We observe that a n = (λ(n ))ρ n for Λ( f) = z n= a nz n. Now, an application of Faber polynomial expansion to the power series S (λ,γ;ϕ) (e.g. see [] or [3, equation (.6)]) yields ( zλ ) ( f) γ Λ( f) = γ F n (a,a 3,a 4,...,a n )z n (.) where F n (a,a 3,...,a n ) = n= i i...(n )i n =n ( ) A(i,i,...,i n ) a i a i 3...a i n n A(i,i,...,i n ) := ( ) (n )i...ni n (i i... i n )!(n ). (i!)(i!)...(i n!) The first few terms of F n (a,a 3,...,a n ) are F = a, F = a a 3, F 3 = a 3 3a a 3 3a 4, F 4 = a 4 4a a 3 4a a 4 a 3 4a 5, F 5 = a 5 5a3 a 3 5a a 4 5 ( a 3 a 5) a 5a 3 a 4 5a 6. By the same token, the coefficients of the inverse map g = f may be expressed by where K n n = g(w) = f (w) = w n= n K n n (a,a 3,...,a n )w n = w n= τ n w n ( n)! ( n)! ( n)!(n )! an (( n))!(n 3)! an 3 a 3 ( n)! ( n)! [ ( n3)!(n 4)! an 4 a 4 (( n))!(n 5)! an 5 a5 ( n)a 3] ( n)! ( n5)!(n 6)! an 6 [a 6 ( n5)a 3 a 4 ] a n j V j V j for 7 j n is a homogeneous polynomial in the variables a 3,a 4,...,a n. Obviously, ( wλ ) (g(w)) γ Λ(g(w)) = γ F n (b,b 3,b 4,...,b n )w n (.) where b n = (λ(n ))τ n. Since, both functions f its inverse map g = f are in S (λ,γ;ϕ), by the definition of subordination, there exist two Schwarz functions n= j 7
5 FABER POLYNOMIAL COEFFICIENTS FOR GENERALIZED BI-SUBORDINATE FUNCTIONS 649 u = c zc z...c n z n..., u <, z D v(w) = d wd w... d n w n..., v(w) <, w D, so that ( zλ ) ( f) γ Λ( f) = ϕ(u) = Kn (c,c,...,c n,,b,...,b n )z n n= (.3) ( wλ ) (g(w)) γ Λ(g(w)) = ϕ(v(w)) = Kn (d,d,...,d n,,b,...,b n )w n. n= (.4) In general (e.g., see [] [, equation (.6)]), the coefficients Kn p := Kn p (k,k,...,k n,,b,...,b n ) are given by Kn p p! B n p! B n = (p n)!n! kn (p n)!(n )! kn k p! B n (p n)!(n 4)! kn 3 k 3 [ p! B n 3 (p n3)!(n 4)! kn 4 k 4 p n3 k p! (p n4)!(n 5)! kn 5 ] B n [ B n 4 B n 3 k 5 (p n4)k k 3 ] k n j X j j 6 where X j is a homogeneous polynomial of degree j in the variables k,k 3,...,k n. For the coefficients of the Schwarz functions u v(w) we have c n d n (e.g., see [8]). Comparing the corresponding coefficients of (.) (.3) yields γ F n (a,a 3,...,a n ) = Kn (c,c,...,c n,,b,...,b n ) (.5) which under the assumption a m = 0; m n we get γ (n )a n = γ (n )(λ(n ))ρ n = c n. (.6) Similarly, comparing the corresponding coefficients of (.) (.4) gives γ F n (b,b 3,...,b n ) = K n (d,d,...,d n,,b,...,b n ) (.7) which by the hypothesis, we obtain γ (n )b n = d n. Note that, for a m = 0; m n we have b n = a n therefore γ (n )a n = γ (n )(λ(n ))ρ n = d n. (.8)
6 650 E. DENIZ, J. M. JAHANGIRI, S. G. HAMIDI AND S. K. KINA Taking the absolute values of either of the equations (.6) or (.8) we obtain the required bound. To prove our next theorem, we shall need the following well-known lemma (see [8]). LEMMA.. ([8]) Let the function p= n= p nz n be so that Re (p) > 0 for z D. Then for < α <, p α p α p ; α <, ( α) p ; α. (.9) Let ϕ = n= ϕ nz n be a Schwarz function so that ϕ <, z D. Set p = [ ϕ ]/[ ϕ ] where p = n= p nz n is so that Re (p) > 0 for z D. Comparing the corresponding coefficients of powers of z yields p = ϕ p = ( ϕ ϕ). Now, substituting for p p letting η = α in (.9) we obtain ϕ ηϕ ( η) ϕ ; η > 0, (η) ϕ ; η 0. (.0) The following theorem gives bounds for the coefficient body (ρ,ρ 3 ) of the generalized bi-subordinate functions of complex order γ type λ. THEOREM.. Let 0 λ γ C 0}. If both functions f = z n= ρ nz n its inverse map g = f are in S (λ,γ;ϕ) then ρ 3 ρ Proof. For n =, (.5) (.7) imply γ (λ) ; B, γb (λ) ; < B ρ = γc λ ρ = γd λ. (.) For n = 3, the equations (.5) (.7), respectively, imply. (λ)ρ 3 (λ) ρ γ = c B c (.) (λ)ρ 3 (36λ λ )ρ γ = d B d. (.3) Considering (.) we get c = d. Also, from (.), (.3) > 0 we find that [( ρ 3 ρ = γ c B ) ( c d B )] d. (.4) 4(λ)
7 FABER POLYNOMIAL COEFFICIENTS FOR GENERALIZED BI-SUBORDINATE FUNCTIONS 65 Taking the absolute values of both sides of (.4) gives [ ρ 3 ρ γ c B c 4(λ) d B ] d. (.5) If B 0, then for η = B / apply (.0) to (.5) to get [ ( ] [ ( ]} ρ 3 ρ γ B B ) c B B ) d. (.6) 4(λ) yields If B > 0 then (.6) yields ρ 3 ρ γ (λ). If B < 0 then for the maximum values c = d = the inequality (.6) ρ 3 ρ γ B [ 4(λ) ( B B )]} = γ B (λ). If B > 0, then for η = B / apply (.0) to (.5) to get ρ 3 ρ γ B [ ( ] [ ( ]} B B ) c B B ) d. (.7) 4(λ) If B > 0 then (.7) yields ρ 3 αρ γ (λ). If B < 0 then for the maximum values c = d = the inequality (.7) yields ρ 3 ρ γ B [ 4(λ) This concludes the proof of Theorem.. ( B B )]} = γ B (λ). For different values of λ γ, Theorems.. yield the following interesting corollaries. COROLLARY.3. If both functions f its inverse map g = f are in S (γ;ϕ), then ρ n γ (n ), ρ m = 0; m n. Taking ϕ = (Az) (Bz) = (A B)z B(A B)z... in Corollary.3, we obtain the result of Hamidi Jahangiri (see [3]). COROLLARY.4. If both functions f its inverse map g = f are in C (γ;ϕ), then ρ n γ (n )n, ρ m = 0; m n. COROLLARY.5. If both functions f its inverse map g = f are in S [δ,β] C [δ,β], respectively, then ρ n ( β) cosδ (n ) ρ n ( β) cosδ, ρ m = 0; m n. n(n )
8 65 E. DENIZ, J. M. JAHANGIRI, S. G. HAMIDI AND S. K. KINA COROLLARY.6. If both functions f its inverse map g = f are in k SP k U CV, respectively, then for ρ m = 0; m n we have B ρ n Q (n ), ρ 3 ρ ; 0 k <, k 4 ; k =, π π 8(k ) t(t)k (t) ; k > B ρ n Q (n )n, ρ 3 ρ ; 0 k <, 3( k ) 4 ; k =, 3π π 4(k ) t(t)k (t) ; k > where Q is given by (.). Proof. Let f its inverse map g = f be in k SP. We will show that Q Q for k 0. First suppose 0 k <. Since 0 arccosk π we have Q Q = B 3. For k = it is clear that Q Q = 3 <. Finally, for k > we get Q Q = [4K (t)(t 6t) π ] 4. A similar argument can be used to justify the case for t(t)k (t) k U C V. Determination of extremal functions for bi-univalent functions (in general) for bi-subordinate functions (in particular) remains a challenge. R E F E R E N C E S [] H. AIRAULT, Remarks on Faber polynomials, Int. Math. Forum 3 (9 ) (008) , MR [] H. AIRAULT, A. BOUALI, Differential calculus on the Faber polynomials, Bull. Sci. Math. 30 (3) (006) 79, MR5663. [3] H. AIRAULT, J. REN, An algebra of differential operators generating functions on the set of univalent functions, Bull. Sci. Math. 6 (5) (00) , MR9475. [4] R. M. ALI, S. K. LEE, V. RAVICHANDRAN, S. SUPRAMANIAM, Coefficient estimates for biunivalent Ma Minda starlike convex functions, Appl. Math. Lett. 5 (3) (0) , MR [5] S. BULUT, Faber polynomial coefficient estimates for a comprehensive subclass of analytic biunivalent functions, C. R. Acad. Sci. Paris, Ser. I 35 (6) (04) , MR308. [6] M. ÇAĞLAR, H. ORHAN AND N. YAĞMUR, Coefficient bounds for new subclasses of bi-univalent functions, Filomat 7 (7) (03), 65-7, MR [7] E. DENIZ, Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal. () (03) 49 60, MR334. [8] P. L. DUREN, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, vol. 59, Springer, New York, 983, MR [9] G. FABER, Über polynomische Entwickelungen, Math. Ann. 57 (3) (903) , MR56. [0] B. A. FRASIN, M. K. AOUF, New subclasses of bi-univalent functions, Appl. Math. Lett. 4 (0) , MR8037. [] S. G. HAMIDI, J. M. JAHANGIRI, Faber polynomial coefficient estimates for analytic bi-close-toconvex functions, C. R. Acad. Sci. Paris, Ser. I 35 () (04) 7 0, MR [] S. G. HAMIDI, J. M. JAHANGIRI, Faber polynomial coefficient estimates for bi-univalent functions defined by subordinations, Bull. Iran. Math. Soc. 4 (5) (05) 03 9, MR34668.
9 FABER POLYNOMIAL COEFFICIENTS FOR GENERALIZED BI-SUBORDINATE FUNCTIONS 653 [3] S. G. HAMIDI, J. M. JAHANGIRI, Faber polynomial coefficient of bi-subordinate functions, C. R. Acad. Sci. Paris, Ser. I 354 (4), (06) , MR [4] J. M. JAHANGIRI, S. G. HAMIDI, Coefficient estimates for certain classes of bi-univalent functions, Int. J. Math. Math. Sci. (03) Article ID 90560, 4 pages, MR [5] J. M. JAHANGIRI, S. G. HAMIDI, S. A. HALIM, Coefficients of bi-univalent functions with positive real part derivatives, Bull. Malay. Math. Sci. Soc. () 37 (04), no. 3, , MR [6] J. M. JAHANGIRI, S. G. HAMIDI, Faber polynomial coefficient estimates for analytic bi-bazilevic functions, Mat. Vesnik 67 () (05), 3 9, MR [7] J. M. JAHANGIRI, N. MAGESH, J. YAMINI, Fekete-Szego inequalities for classes of bi-starlike bi-convex functions, Electron. J. Math. Anal. Appl. 3 () (05) 33 40, MR [8] S. KANAS, A. WISNIOWSKA, Conic regions k -uniform convexity, J. Math. Anal. Appl. 05 (999) , MR [9] S. S. KUMAR, V. KUMAR AND V. RAVICHANDRAN, Estimates for the initial coefficients of biunivalent functions, Tamsui Oxford J. Inform. Math. Sci. 9 (4) (03) , MR [0] W. C. MA, D. MINDA, A unified treatment of some special classes of univalent functions, Proceedings of the Conference on Complex Analysis (Tianjin, 99), 57 69, Conf. Proc. Lecture Notes Anal. I, Int. Press, Cambridge, MA, 994, MR [] V. RAVICHANDRAN, Y. POLATOĞLU, M. BOLCAL, A. ŞEN, Certain subclasses of starlike convex functions of complex order, Hacettepe J. Math. Stat. 34 (005) 9 5, MR704. [] H. M. SRIVASTAVA, A. K. MISHRA, P. GOCHHAYAT, Certain subclasses of analytic bi-univalent functions, Appl. Math. Lett. 3 (0) (00) 88 9, MR [3] H. M. SRIVASTAVA, S. BULUT, M. ÇAĞLAR, N. YAĞMUR, Coefficient estimates for a general subclass of analytic bi-univalent functions, Filomat 7 (5) (03) 83 84, MR3860. [4] H. M. SRIVASTAVA, S. S. EKER, R. M. ALI, Coefficient bounds for a certain class of analytic bi-univalent functions, Filomat 9 (8) (05) , MR [5] P. ZAPRAWA, On the Fekete Szegö problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin () (04) 69 78, MR [6] Q.-H. XU, Y.-C. GUI, H. M. SRIVASTAVA, Coefficient estimates for a certain subclass of analytic bi-univalent functions, Appl. Math. Lett. 5 (0) , MR [7] Q.-H. XU, H.-G. XIAO, H. M. SRIVASTAVA, A certain general subclass of analytic bi-univalent functions associated coefficient estimate problems, Appl. Math. Comput. 8 (0) , MR (Received October 0, 06) Erhan Deniz Department of Mathematics Faculty of Science Letters, Kafkas University Kars, Turkey edeniz36@gmail.com Jay M. Jahangiri Department of Mathematical Sciences Kent State University Burton, OH440, USA jjahangi@kent.edu Samaneh G. Hamidi Department of Mathematics Brigham Young University Provo, UT84604, USA s.hamidi 6@yahoo.com Sibel K. Kına Department of Mathematics Faculty of Science Letters, Kafkas University Kars, Turkey sibelyuksel08@gmail.com Journal of Mathematical Inequalities jmi@ele-math.com
COEFFICIENT ESTIMATES FOR A SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS
Bull. Korean Math. Soc. 0 (0), No. 0, pp. 1 0 https://doi.org/10.4134/bkms.b170051 pissn: 1015-8634 / eissn: 2234-3016 COEFFICIENT ESTIMATES FOR A SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS Ebrahim Analouei
More informationFaber polynomial coefficient bounds for a subclass of bi-univalent functions
Stud. Univ. Babeş-Bolyai Math. 6(06), No., 37 Faber polynomial coefficient bounds for a subclass of bi-univalent functions Şahsene Altınkaya Sibel Yalçın Abstract. In this ork, considering a general subclass
More informationCoefficient Bounds for a Certain Class of Analytic and Bi-Univalent Functions
Filomat 9:8 (015), 1839 1845 DOI 10.98/FIL1508839S Published by Faculty of Sciences Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Coefficient Bounds for a Certain
More informationInitial Coefficient Bounds for a General Class of Bi-Univalent Functions
Filomat 29:6 (2015), 1259 1267 DOI 10.2298/FIL1506259O Published by Faculty of Sciences Mathematics, University of Niš, Serbia Available at: http://.pmf.ni.ac.rs/filomat Initial Coefficient Bounds for
More informationCOEFFICIENT BOUNDS FOR A SUBCLASS OF BI-UNIVALENT FUNCTIONS
TWMS J. Pure Appl. Math., V.6, N.2, 205, pp.80-85 COEFFICIENT BOUNDS FOR A SUBCLASS OF BI-UNIVALENT FUNCTIONS ŞAHSENE ALTINKAYA, SIBEL YALÇIN Abstract. An analytic function f defined on the open unit disk
More informationResearch Article Coefficient Estimates for Two New Subclasses of Biunivalent Functions with respect to Symmetric Points
Function Spaces Volume 2015 Article ID 145242 5 pages http://dx.doi.org/10.1155/2015/145242 Research Article Coefficient Estimates for Two New Subclasses of Biunivalent Functions with respect to Symmetric
More informationFABER POLYNOMIAL COEFFICIENT ESTIMATES FOR A NEW SUBCLASS OF MEROMORPHIC BI-UNIVALENT FUNCTIONS ADNAN GHAZY ALAMOUSH, MASLINA DARUS
Available online at http://scik.org Adv. Inequal. Appl. 216, 216:3 ISSN: 25-7461 FABER POLYNOMIAL COEFFICIENT ESTIMATES FOR A NEW SUBCLASS OF MEROMORPHIC BI-UNIVALENT FUNCTIONS ADNAN GHAZY ALAMOUSH, MASLINA
More informationON ESTIMATE FOR SECOND AND THIRD COEFFICIENTS FOR A NEW SUBCLASS OF ANALYTIC AND BI-UNIVALENT FUNCTIONS BY USING DIFFERENTIAL OPERATORS
Palestine Journal of Mathematics Vol. 8(1)(019), 44 51 Palestine Polytechnic University-PPU 019 ON ESTIMATE FOR SECOND AND THIRD COEFFICIENTS FOR A NEW SUBCLASS OF ANALYTIC AND BI-UNIVALENT FUNCTIONS BY
More informationORDER. 1. INTRODUCTION Let A denote the class of functions of the form
SARAJEVO JOURNAL OF MATHEMATICS Vol.10 (22) (2014), 55 60 DOI: 10.5644/SJM.10.1.07 ON UNIFIED CLASS OF γ-spirallike FUNCTIONS OF COMPLEX ORDER T. M. SEOUDY ABSTRACT. In this paper, we obtain a necessary
More informationA Certain Subclass of Analytic Functions Defined by Means of Differential Subordination
Filomat 3:4 6), 3743 3757 DOI.98/FIL64743S Published by Faculty of Sciences Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat A Certain Subclass of Analytic Functions
More informationarxiv: v1 [math.cv] 1 Nov 2017
arxiv:7.0074v [math.cv] Nov 07 The Fekete Szegö Coefficient Inequality For a New Class of m-fold Symmetric Bi-Univalent Functions Satisfying Subordination Condition Arzu Akgül Department of Mathematics,
More informationarxiv: v1 [math.cv] 30 Sep 2017
SUBCLASSES OF BI-UNIVALENT FUNCTIONS DEFINED BY SĂLĂGEAN TYPE DIFFERENCE OPERATOR G. MURUGUSUNDARAMOORTHY, AND K. VIJAYA 2, arxiv:70.0043v [math.cv] 30 Sep 207 Corresponding Author,2 School of Advanced
More informationSubclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers
Acta Univ. Sapientiae, Mathematica, 10, 1018 70-84 DOI: 10.478/ausm-018-0006 Subclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers H. Özlem Güney Dicle University,
More informationSECOND HANKEL DETERMINANT FOR A CERTAIN SUBCLASS OF ANALYTIC AND BI-UNIVALENT FUNCTIONS
TWMS J Pure Appl Math V7, N, 06, pp85-99 SECOND HANKEL DETERMINANT FOR A CERTAIN SUBCLASS OF ANALYTIC AND BI-UNIVALENT FUNCTIONS BA FRASIN, K VIJAYA, M KASTHURI Abstract In the present paper, we consider
More informationTHE FEKETE-SZEGÖ COEFFICIENT FUNCTIONAL FOR TRANSFORMS OF ANALYTIC FUNCTIONS. Communicated by Mohammad Sal Moslehian. 1.
Bulletin of the Iranian Mathematical Society Vol. 35 No. (009 ), pp 119-14. THE FEKETE-SZEGÖ COEFFICIENT FUNCTIONAL FOR TRANSFORMS OF ANALYTIC FUNCTIONS R.M. ALI, S.K. LEE, V. RAVICHANDRAN AND S. SUPRAMANIAM
More informationOn a subclass of analytic functions involving harmonic means
DOI: 10.1515/auom-2015-0018 An. Şt. Univ. Ovidius Constanţa Vol. 231),2015, 267 275 On a subclass of analytic functions involving harmonic means Andreea-Elena Tudor Dorina Răducanu Abstract In the present
More informationSecond Hankel determinant for the class of Bazilevic functions
Stud. Univ. Babeş-Bolyai Math. 60(2015), No. 3, 413 420 Second Hankel determinant for the class of Bazilevic functions D. Vamshee Krishna and T. RamReddy Abstract. The objective of this paper is to obtain
More informationON CERTAIN CLASS OF UNIVALENT FUNCTIONS WITH CONIC DOMAINS INVOLVING SOKÓ L - NUNOKAWA CLASS
U.P.B. Sci. Bull., Series A, Vol. 80, Iss. 1, 018 ISSN 13-707 ON CERTAIN CLASS OF UNIVALENT FUNCTIONS WITH CONIC DOMAINS INVOLVING SOKÓ L - NUNOKAWA CLASS S. Sivasubramanian 1, M. Govindaraj, K. Piejko
More informationCERTAIN SUBCLASSES OF STARLIKE AND CONVEX FUNCTIONS OF COMPLEX ORDER
Hacettepe Journal of Mathematics and Statistics Volume 34 (005), 9 15 CERTAIN SUBCLASSES OF STARLIKE AND CONVEX FUNCTIONS OF COMPLEX ORDER V Ravichandran, Yasar Polatoglu, Metin Bolcal, and Aru Sen Received
More informationCoecient bounds for certain subclasses of analytic functions of complex order
Hacettepe Journal of Mathematics and Statistics Volume 45 (4) (2016), 1015 1022 Coecient bounds for certain subclasses of analytic functions of complex order Serap Bulut Abstract In this paper, we introduce
More informationRosihan M. Ali and V. Ravichandran 1. INTRODUCTION
TAIWANESE JOURNAL OF MATHEMATICS Vol. 14, No. 4, pp. 1479-1490, August 2010 This paper is available online at http://www.tjm.nsysu.edu.tw/ CLASSES OF MEROMORPHIC α-convex FUNCTIONS Rosihan M. Ali and V.
More informationOn the Second Hankel Determinant for the kth-root Transform of Analytic Functions
Filomat 3: 07 7 5 DOI 098/FIL707A Published by Faculty of Sciences and Mathematics University of Niš Serbia Available at: http://wwwpmfniacrs/filomat On the Second Hankel Determinant for the kth-root Transform
More informationON THE FEKETE-SZEGÖ INEQUALITY FOR A CLASS OF ANALYTIC FUNCTIONS DEFINED BY USING GENERALIZED DIFFERENTIAL OPERATOR
Acta Universitatis Apulensis ISSN: 58-539 No. 6/0 pp. 67-78 ON THE FEKETE-SZEGÖ INEQUALITY FOR A CLASS OF ANALYTIC FUNCTIONS DEFINED BY USING GENERALIZED DIFFERENTIAL OPERATOR Salma Faraj Ramadan, Maslina
More informationCoefficient Estimates for Bazilevič Ma-Minda Functions in the Space of Sigmoid Function
Malaya J. Mat. 43)206) 505 52 Coefficient Estimates for Bazilevič Ma-Minda Functions in the Space of Sigmoid Function Sunday Oluwafemi Olatunji a, and Emmanuel Jesuyon Dansu b a,b Department of Mathematical
More informationCorrespondence should be addressed to Serap Bulut;
The Scientific World Journal Volume 201, Article ID 17109, 6 pages http://dx.doi.org/10.1155/201/17109 Research Article Coefficient Estimates for Initial Taylor-Maclaurin Coefficients for a Subclass of
More informationCOEFFICIENTS OF BI-UNIVALENT FUNCTIONS INVOLVING PSEUDO-STARLIKENESS ASSOCIATED WITH CHEBYSHEV POLYNOMIALS
Khayyam J. Math. 5 (2019), no. 1, 140 149 DOI: 10.2204/kjm.2019.8121 COEFFICIENTS OF BI-UNIVALENT FUNCTIONS INVOLVING PSEUDO-STARLIKENESS ASSOCIATED WITH CHEBYSHEV POLYNOMIALS IBRAHIM T. AWOLERE 1, ABIODUN
More informationCoefficient bounds for some subclasses of p-valently starlike functions
doi: 0.2478/v0062-02-0032-y ANNALES UNIVERSITATIS MARIAE CURIE-SKŁODOWSKA LUBLIN POLONIA VOL. LXVII, NO. 2, 203 SECTIO A 65 78 C. SELVARAJ, O. S. BABU G. MURUGUSUNDARAMOORTHY Coefficient bounds for some
More informationarxiv: v1 [math.cv] 19 Jul 2012
arxiv:1207.4529v1 [math.cv] 19 Jul 2012 On the Radius Constants for Classes of Analytic Functions 1 ROSIHAN M. ALI, 2 NAVEEN KUMAR JAIN AND 3 V. RAVICHANDRAN 1,3 School of Mathematical Sciences, Universiti
More informationFUNCTIONS WITH NEGATIVE COEFFICIENTS
A NEW SUBCLASS OF k-uniformly CONVEX FUNCTIONS WITH NEGATIVE COEFFICIENTS H. M. SRIVASTAVA T. N. SHANMUGAM Department of Mathematics and Statistics University of Victoria British Columbia 1V8W 3P4, Canada
More informationOn a new class of (j, i)-symmetric function on conic regions
Available online at wwwisr-publicationscom/jnsa J Nonlinear Sci Appl 10 (2017) 4628 4637 Research Article Journal Homepage: wwwtjnsacom - wwwisr-publicationscom/jnsa On a new class of (j i)-symmetric function
More informationFekete-Szegö Problem for Certain Subclass of Analytic Univalent Function using Quasi-Subordination
Mathematica Aeterna, Vol. 3, 203, no. 3, 93-99 Fekete-Szegö Problem for Certain Subclass of Analytic Univalent Function using Quasi-Subordination B. Srutha Keerthi Department of Applied Mathematics Sri
More informationCertain properties of a new subclass of close-to-convex functions
Arab J Math (212) 1:39 317 DOI 1.17/s465-12-29-y RESEARCH ARTICLE Pranay Goswami Serap Bulut Teodor Bulboacă Certain properties of a new subclass of close-to-convex functions Received: 18 November 211
More informationSUBORDINATION RESULTS FOR CERTAIN SUBCLASSES OF UNIVALENT MEROMORPHIC FUNCTIONS
SUBORDINATION RESULTS FOR CERTAIN SUBCLASSES OF UNIVALENT MEROMORPHIC FUNCTIONS, P.G. Student, Department of Mathematics,Science College, Salahaddin University, Erbil, Region of Kurdistan, Abstract: In
More informationCOEFFICIENT INEQUALITY FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS
NEW ZEALAND JOURNAL OF MATHEMATICS Volume 42 (2012), 217-228 COEFFICIENT INEQUALITY FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS D. VAMSHEE KRISHNA 1 and T. RAMREDDY (Received 12 December, 2012) Abstract.
More informationDifferential Operator of a Class of Meromorphic Univalent Functions With Negative Coefficients
Differential Operator of a Class of Meromorphic Univalent Functions With Negative Coefficients Waggas Galib Atshan and Ali Hamza Abada Department of Mathematics College of Computer Science and Mathematics
More informationSOME INCLUSION PROPERTIES OF STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH HOHLOV OPERATOR. II
italian journal of pure and applied mathematics n. 37 2017 117 126 117 SOME INCLUSION PROPERTIES OF STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH HOHLOV OPERATOR. II M. Kasthuri K. Vijaya 1 K. Uma School
More informationThe Relationships Between p valent Functions and Univalent Functions
DOI:.55/auom-25-5 An. Şt. Univ. Ovidius Constanţa Vol. 23(),25, 65 72 The Relationships Between p valent Functions and Univalent Functions Murat ÇAĞLAR Abstract In this paper, we obtain some sufficient
More informationHARMONIC CLOSE-TO-CONVEX MAPPINGS
Applied Mathematics Stochastic Analysis, 15:1 (2002, 23-28. HARMONIC CLOSE-TO-CONVEX MAPPINGS JAY M. JAHANGIRI 1 Kent State University Department of Mathematics Burton, OH 44021-9500 USA E-mail: jay@geauga.kent.edu
More informationOn Starlike and Convex Functions with Respect to 2k-Symmetric Conjugate Points
Tamsui Oxford Journal of Mathematical Sciences 24(3) (28) 277-287 Aletheia University On Starlike and Convex Functions with espect to 2k-Symmetric Conjugate Points Zhi-Gang Wang and Chun-Yi Gao College
More informationOn neighborhoods of functions associated with conic domains
DOI: 0.55/auom-205-0020 An. Şt. Univ. Ovidius Constanţa Vol. 23(),205, 29 30 On neighborhoods of functions associated with conic domains Nihat Yağmur Abstract Let k ST [A, B], k 0, B < A be the class of
More informationCOEFFICIENT INEQUALITY FOR CERTAIN SUBCLASS OF ANALYTIC FUNCTIONS
Armenian Journal of Mathematics Volume 4, Number 2, 2012, 98 105 COEFFICIENT INEQUALITY FOR CERTAIN SUBCLASS OF ANALYTIC FUNCTIONS D Vamshee Krishna* and T Ramreddy** * Department of Mathematics, School
More informationSome properties for α-starlike functions with respect to k-symmetric points of complex order
doi: 1.17951/a.217.71.1.1 A N N A L E S U N I V E R S I T A T I S M A R I A E C U R I E - S K Ł O D O W S K A L U B L I N P O L O N I A VOL. LXXI, NO. 1, 217 SECTIO A 1 9 H. E. DARWISH, A. Y. LASHIN and
More informationESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF CERTAIN SUBCLASSES OF BI-UNIVALENT FUNCTIONS
Miskolc Matheatical Notes HU e-issn 787-43 Vol. 7 (07), No., pp. 739 748 DOI: 0.854/MMN.07.565 ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF CERTAIN SUBCLASSES OF BI-UNIVALENT FUNCTIONS BADR S. ALKAHTANI,
More informationAPPLYING RUSCHEWEYH DERIVATIVE ON TWO SUB-CLASSES OF BI-UNIVALENT FUNCTIONS
International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:1 No:06 68 APPLYING RUSCHEWEYH DERIVATIVE ON TWO SUB-CLASSES OF BI-UNIVALENT FUNCTIONS ABDUL RAHMAN S. JUMA 1, FATEH S. AZIZ DEPARTMENT
More informationA Note on Coefficient Inequalities for (j, i)-symmetrical Functions with Conic Regions
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4874 ISSN (o) 2303-4955 wwwimviblorg /JOURNALS / BULLETIN Vol 6(2016) 77-87 Former BULLETIN OF THE SOCIETY OF MATHEMATICIANS BANJA
More informationSUBCLASS OF HARMONIC STARLIKE FUNCTIONS ASSOCIATED WITH SALAGEAN DERIVATIVE
LE MATEMATICHE Vol. LXIX (2014) Fasc. II, pp. 147 158 doi: 10.4418/2014.69.2.13 SUBCLASS OF HARMONIC STARLIKE FUNCTIONS ASSOCIATED WITH SALAGEAN DERIVATIVE H. E. DARWISH - A. Y. LASHIN - S. M. SOILEH The
More informationNotes on Starlike log-harmonic Functions. of Order α
Int. Journal of Math. Analysis, Vol. 7, 203, no., 9-29 Notes on Starlike log-harmonic Functions of Order α Melike Aydoğan Department of Mathematics Işık University, Meşrutiyet Koyu Şile İstanbul, Turkey
More informationSufficient conditions for starlike functions associated with the lemniscate of Bernoulli
Kumar et al. Journal of Inequalities and Applications 2013, 2013:176 R E S E A R C H Open Access Sufficient conditions for starlike functions associated with the lemniscate of Bernoulli S Sivaprasad Kumar
More informationFekete-Szegö Inequality for Certain Classes of Analytic Functions Associated with Srivastava-Attiya Integral Operator
Applied Mathematical Sciences, Vol. 9, 015, no. 68, 3357-3369 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ams.015.543 Fekete-Szegö Inequality for Certain Classes of Analytic Functions Associated
More informationA note on a subclass of analytic functions defined by a generalized Sălăgean and Ruscheweyh operator
General Mathematics Vol. 17, No. 4 (2009), 75 81 A note on a subclass of analytic functions defined by a generalized Sălăgean and Ruscheweyh operator Alina Alb Lupaş, Adriana Cătaş Abstract By means of
More informationA NEW SUBCLASS OF MEROMORPHIC FUNCTION WITH POSITIVE COEFFICIENTS
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 32010), Pages 109-121. A NEW SUBCLASS OF MEROMORPHIC FUNCTION WITH POSITIVE COEFFICIENTS S.
More informationarxiv: v3 [math.cv] 11 Aug 2014
File: SahSha-arXiv_Aug2014.tex, printed: 27-7-2018, 3.19 ON MAXIMAL AREA INTEGRAL PROBLEM FOR ANALYTIC FUNCTIONS IN THE STARLIKE FAMILY S. K. SAHOO AND N. L. SHARMA arxiv:1405.0469v3 [math.cv] 11 Aug 2014
More informationOn a subclass of certain p-valent starlike functions with negative coefficients 1
General Mathematics Vol. 18, No. 2 (2010), 95 119 On a subclass of certain p-valent starlike functions with negative coefficients 1 S. M. Khairnar, N. H. More Abstract We introduce the subclass T Ω (n,
More informationarxiv: v2 [math.cv] 24 Nov 2017
adii of the β uniformly convex of order α of Lommel and Struve functions Sercan Topkaya, Erhan Deniz and Murat Çağlar arxiv:70.0975v [math.cv] 4 Nov 07 Department of Mathematics, Faculty of Science and
More informationSecond Hankel determinant obtained with New Integral Operator defined by Polylogarithm Function
Global Journal of Pure and Applied Mathematics. ISSN 0973-768 Volume 3, Number 7 (07), pp. 3467-3475 Research India Publications http://www.ripublication.com/gjpam.htm Second Hankel determinant obtained
More informationSome Further Properties for Analytic Functions. with Varying Argument Defined by. Hadamard Products
International Mathematical Forum, Vol. 10, 2015, no. 2, 75-93 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2015.412205 Some Further Properties for Analytic Functions with Varying Argument
More informationDIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF ANALYTIC FUNCTIONS DEFINED BY THE MULTIPLIER TRANSFORMATION
M athematical I nequalities & A pplications Volume 12, Number 1 2009), 123 139 DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF ANALYTIC FUNCTIONS DEFINED BY THE MULTIPLIER TRANSFORMATION ROSIHAN M. ALI,
More informationInclusion and argument properties for certain subclasses of multivalent functions defined by the Dziok-Srivastava operator
Advances in Theoretical Alied Mathematics. ISSN 0973-4554 Volume 11, Number 4 016,. 361 37 Research India Publications htt://www.riublication.com/atam.htm Inclusion argument roerties for certain subclasses
More informationCoefficient Inequalities of Second Hankel Determinants for Some Classes of Bi-Univalent Functions
mathematics Article Coefficient Inequalities of Second Hankel Determinants for Some Classes of Bi-Univalent Functions Rayaprolu Bharavi Sharma Kalikota Rajya Laxmi, * Department of Mathematics, Kakatiya
More informationCertain subclasses of uniformly convex functions and corresponding class of starlike functions
Malaya Journal of Matematik 1(1)(2013) 18 26 Certain subclasses of uniformly convex functions and corresponding class of starlike functions N Magesh, a, and V Prameela b a PG and Research Department of
More informationarxiv: v1 [math.cv] 11 Aug 2017
CONSTRUCTION OF TOEPLITZ MATRICES WHOSE ELEMENTS ARE THE COEFFICIENTS OF UNIVALENT FUNCTIONS ASSOCIATED WITH -DERIVATIVE OPERATOR arxiv:1708.03600v1 [math.cv] 11 Aug 017 NANJUNDAN MAGESH 1, ŞAHSENE ALTINKAYA,,
More informationInt. J. Open Problems Complex Analysis, Vol. 3, No. 1, March 2011 ISSN ; Copyright c ICSRS Publication,
Int. J. Open Problems Complex Analysis, Vol. 3, No. 1, March 211 ISSN 274-2827; Copyright c ICSRS Publication, 211 www.i-csrs.org Coefficient Estimates for Certain Class of Analytic Functions N. M. Mustafa
More informationMajorization Properties for Subclass of Analytic p-valent Functions Defined by the Generalized Hypergeometric Function
Tamsui Oxford Journal of Information and Mathematical Sciences 284) 2012) 395-405 Aletheia University Majorization Properties for Subclass of Analytic p-valent Functions Defined by the Generalized Hypergeometric
More informationSecond Hankel Determinant Problem for a Certain Subclass of Univalent Functions
International Journal of Mathematical Analysis Vol. 9, 05, no. 0, 493-498 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/ijma.05.55 Second Hankel Determinant Problem for a Certain Subclass of Univalent
More informationSubclass of Meromorphic Functions with Positive Coefficients Defined by Frasin and Darus Operator
Int. J. Open Problems Complex Analysis, Vol. 8, No. 1, March 2016 ISSN 2074-2827; Copyright c ICSRS Publication, 2016 www.i-csrs.org Subclass of Meromorphic Functions with Positive Coefficients Defined
More informationConvolution properties for subclasses of meromorphic univalent functions of complex order. Teodor Bulboacă, Mohamed K. Aouf, Rabha M.
Faculty of Sciences Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Filomat 26:1 (2012), 153 163 DOI: 10.2298/FIL1201153B Convolution properties for subclasses of meromorphic
More informationConvex Functions and Functions with Bounded Turning
Tamsui Oxford Journal of Mathematical Sciences 26(2) (2010) 161-172 Aletheia University Convex Functions Functions with Bounded Turning Nikola Tuneski Faculty of Mechanical Engineering, Karpoš II bb, 1000
More informationTHIRD HANKEL DETERMINANT FOR THE INVERSE OF RECIPROCAL OF BOUNDED TURNING FUNCTIONS HAS A POSITIVE REAL PART OF ORDER ALPHA
ISSN 074-1871 Уфимский математический журнал. Том 9. т (017). С. 11-11. THIRD HANKEL DETERMINANT FOR THE INVERSE OF RECIPROCAL OF BOUNDED TURNING FUNCTIONS HAS A POSITIVE REAL PART OF ORDER ALPHA B. VENKATESWARLU,
More informationAn Investigation on Minimal Surfaces of Multivalent Harmonic Functions 1
General Mathematics Vol. 19, No. 1 (2011), 99 107 An Investigation on Minimal Surfaces of Multivalent Harmonic Functions 1 Hakan Mete Taştan, Yaşar Polato glu Abstract The projection on the base plane
More informationSUBCLASSES OF P-VALENT STARLIKE FUNCTIONS DEFINED BY USING CERTAIN FRACTIONAL DERIVATIVE OPERATOR
Sutra: International Journal of Mathematical Science Education Technomathematics Research Foundation Vol. 4 No. 1, pp. 17-32, 2011 SUBCLASSES OF P-VALENT STARLIKE FUNCTIONS DEFINED BY USING CERTAIN FRACTIONAL
More informationHankel determinant for p-valently starlike and convex functions of order α
General Mathematics Vol. 17, No. 4 009, 9 44 Hankel determinant for p-valently starlike and convex functions of order α Toshio Hayami, Shigeyoshi Owa Abstract For p-valently starlike and convex functions
More informationDifferential Subordination and Superordination Results for Certain Subclasses of Analytic Functions by the Technique of Admissible Functions
Filomat 28:10 (2014), 2009 2026 DOI 10.2298/FIL1410009J Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: htt://www.mf.ni.ac.rs/filomat Differential Subordination
More informationA NOTE ON A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY A GENERALIZED SĂLĂGEAN OPERATOR. Alina Alb Lupaş, Adriana Cătaş
Acta Universitatis Apulensis ISSN: 158-539 No. /010 pp. 35-39 A NOTE ON A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY A GENERALIZED SĂLĂGEAN OPERATOR Alina Alb Lupaş, Adriana Cătaş Abstract. By means of
More informationA Certain Subclass of Multivalent Functions Involving Higher-Order Derivatives
Filomat 30:1 (2016), 113 124 DOI 10.2298/FIL1601113S Published by Faculty of Sciences Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat A Certain Subclass of Multivalent
More informationSOME SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY GENERALIZED DIFFERENTIAL OPERATOR. Maslina Darus and Imran Faisal
Acta Universitatis Apulensis ISSN: 1582-5329 No. 29/212 pp. 197-215 SOME SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY GENERALIZED DIFFERENTIAL OPERATOR Maslina Darus and Imran Faisal Abstract. Let A denote
More informationOn certain subclasses of analytic functions associated with generalized struve functions
BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Number 3(79), 2015, Pages 3 13 ISSN 1024 7696 On certain subclasses of analytic functions associated with generalized struve functions G.
More informationCertain classes of p-valent analytic functions with negative coefficients and (λ, p)-starlike with respect to certain points
BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Number 379), 2015, Pages 35 49 ISSN 1024 7696 Certain classes of p-valent analytic functions with negative coefficients and λ, p)-starlike
More informationBulletin of the Transilvania University of Braşov Vol 8(57), No Series III: Mathematics, Informatics, Physics, 1-12
Bulletin of the Transilvania University of Braşov Vol 857), No. 2-2015 Series III: Mathematics, Informatics, Physics, 1-12 DISTORTION BOUNDS FOR A NEW SUBCLASS OF ANALYTIC FUNCTIONS AND THEIR PARTIAL SUMS
More informationSUBCLASS OF HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH THE DERIVATIVE OPERATOR
Hacettepe Journal of Mathematics and Statistics Volume 41(1) (2012), 47 58 SUBCLASS OF HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH THE DERIVATIVE OPERATOR A.L. Pathak, S.B. Joshi, Preeti Dwivedi and R.
More informationSOME CLASSES OF MEROMORPHIC MULTIVALENT FUNCTIONS WITH POSITIVE COEFFICIENTS INVOLVING CERTAIN LINEAR OPERATOR
International Journal of Basic & Alied Sciences IJBAS-IJENS Vol:13 No:03 56 SOME CLASSES OF MEROMORPHIC MULTIVALENT FUNCTIONS WITH POSITIVE COEFFICIENTS INVOLVING CERTAIN LINEAR OPERATOR Abdul Rahman S
More informationOn Multivalent Functions Associated with Fixed Second Coefficient and the Principle of Subordination
International Journal of Mathematical Analysis Vol. 9, 015, no. 18, 883-895 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ijma.015.538 On Multivalent Functions Associated with Fixed Second Coefficient
More informationCoefficient Inequalities of a Subclass of Starlike Functions Involving q - Differential Operator
Advances in Analysis, Vol. 3, No., April 018 https://dx.doi.org/10.606/aan.018.300 73 Coefficient Inequalities of a Subclass of Starlike Functions Involving q - Differential Operator K. R. Karthikeyan
More informationCoefficient Inequalities for Classes of Uniformly. Starlike and Convex Functions Defined by Generalized. Ruscheweyh Operator
International Mathematical Forum, Vol. 6, 2011, no. 65, 3227-3234 Coefficient Inequalities for Classes of Uniformly Starlike Convex Functions Defined by Generalized Ruscheweyh Operator Hesam Mahzoon Department
More informationON POLYHARMONIC UNIVALENT MAPPINGS
ON POLYHARMONIC UNIVALENT MAPPINGS J. CHEN, A. RASILA and X. WANG In this paper, we introduce a class of complex-valued polyharmonic mappings, denoted by HS pλ, and its subclass HS 0 pλ, where λ [0, ]
More informationSubordination and Superordination Results for Analytic Functions Associated With Convolution Structure
Int. J. Open Problems Complex Analysis, Vol. 2, No. 2, July 2010 ISSN 2074-2827; Copyright c ICSRS Publication, 2010 www.i-csrs.org Subordination and Superordination Results for Analytic Functions Associated
More informationAn ordinary differentail operator and its applications to certain classes of multivalently meromorphic functions
Bulletin of Mathematical analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 1, Issue 2, (2009), Pages 17-22 An ordinary differentail operator and its applications to certain
More informationOn Certain Class of Meromorphically Multivalent Reciprocal Starlike Functions Associated with the Liu-Srivastava Operator Defined by Subordination
Filomat 8:9 014, 1965 198 DOI 10.98/FIL1409965M Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat On Certain Class of Meromorphically
More informationA New Subclasses of Meromorphic p-valent Functions with Positive Coefficient Defined by Fractional Calculus Operators
Volume 119 No. 15 2018, 2447-2461 ISSN: 1314-3395 (on-line version) url: http://www.acadpubl.eu/hub/ http://www.acadpubl.eu/hub/ A New Subclasses of Meromorphic p-valent Functions with Positive Coefficient
More informationOn Quasi-Hadamard Product of Certain Classes of Analytic Functions
Bulletin of Mathematical analysis Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 1, Issue 2, (2009), Pages 36-46 On Quasi-Hadamard Product of Certain Classes of Analytic Functions Wei-Ping
More informationA NEW CLASS OF MEROMORPHIC FUNCTIONS RELATED TO CHO-KWON-SRIVASTAVA OPERATOR. F. Ghanim and M. Darus. 1. Introduction
MATEMATIQKI VESNIK 66, 1 14, 9 18 March 14 originalni nauqni rad research paper A NEW CLASS OF MEROMORPHIC FUNCTIONS RELATED TO CHO-KWON-SRIVASTAVA OPERATOR F. Ghanim and M. Darus Abstract. In the present
More informationNEW SUBCLASS OF MULTIVALENT HYPERGEOMETRIC MEROMORPHIC FUNCTIONS
Kragujevac Journal of Mathematics Volume 42(1) (2018), Pages 83 95. NEW SUBCLASS OF MULTIVALENT HYPERGEOMETRIC MEROMORPHIC FUNCTIONS M. ALBEHBAH 1 AND M. DARUS 2 Abstract. In this aer, we introduce a new
More informationConvolution Properties of Convex Harmonic Functions
Int. J. Open Problems Complex Analysis, Vol. 4, No. 3, November 01 ISSN 074-87; Copyright c ICSRS Publication, 01 www.i-csrs.org Convolution Properties of Convex Harmonic Functions Raj Kumar, Sushma Gupta
More informationSome basic properties of certain subclasses of meromorphically starlike functions
Wang et al. Journal of Inequalities Applications 2014, 2014:29 R E S E A R C H Open Access Some basic properties of certain subclasses of meromorphically starlike functions Zhi-Gang Wang 1*, HM Srivastava
More informationarxiv: v1 [math.cv] 22 Apr 2009
arxiv:94.3457v [math.cv] 22 Apr 29 CERTAIN SUBCLASSES OF CONVEX FUNCTIONS WITH POSITIVE AND MISSING COEFFICIENTS BY USING A FIXED POINT SH. NAJAFZADEH, M. ESHAGHI GORDJI AND A. EBADIAN Abstract. By considering
More informationPROPERTIES AND CHARACTERISTICS OF A FAMILY CONSISTING OF BAZILEVIĆ (TYPE) FUNCTIONS SPECIFIED BY CERTAIN LINEAR OPERATORS
Electronic Journal of Mathematical Analysis and Applications Vol. 7) July 019, pp. 39-47. ISSN: 090-79X online) http://math-frac.org/journals/ejmaa/ PROPERTIES AND CHARACTERISTICS OF A FAMILY CONSISTING
More informationOn a New Subclass of Salagean Type Analytic Functions
Int. Journal of Math. Analysis, Vol. 3, 2009, no. 14, 689-700 On a New Subclass of Salagean Type Analytic Functions K. K. Dixit a, V. Kumar b, A. L. Pathak c and P. Dixit b a Department of Mathematics,
More informationDIFFERENTIAL OPERATOR GENERALIZED BY FRACTIONAL DERIVATIVES
Miskolc Mathematical Notes HU e-issn 1787-2413 Vol. 12 (2011), No. 2, pp. 167 184 DIFFERENTIAL OPERATOR GENERALIZED BY FRACTIONAL DERIVATIVES RABHA W. IBRAHIM AND M. DARUS Received March 30, 2010 Abstract.
More informationConvolutions of harmonic right half-plane mappings
Open Math. 06; 4 789 800 Open Mathematics Open Access Research Article YingChun Li and ZhiHong Liu* Convolutions of harmonic right half-plane mappings OI 0.55/math-06-0069 Received March, 06; accepted
More informationMeromorphic parabolic starlike functions with a fixed point involving Srivastava-Attiya operator
Malaya J. Mat. 2(2)(2014) 91 102 Meromorphic parabolic starlike functions with a fixed point involving Srivastava-Attiya operator G. Murugusundaramoorthy a, and T. Janani b a,b School of Advanced Sciences,
More informationDifferential Subordinations and Harmonic Means
Bull. Malays. Math. Sci. Soc. (2015) 38:1243 1253 DOI 10.1007/s40840-014-0078-9 Differential Subordinations and Harmonic Means Stanisława Kanas Andreea-Elena Tudor eceived: 9 January 2014 / evised: 3 April
More information