On a subclass of analytic functions involving harmonic means
|
|
- Damon Marshall
- 5 years ago
- Views:
Transcription
1 DOI: /auom An. Şt. Univ. Ovidius Constanţa Vol. 231),2015, On a subclass of analytic functions involving harmonic means Andreea-Elena Tudor Dorina Răducanu Abstract In the present paper, we consider a generalised subclass of analytic functions involving arithmetic, geometric harmonic means. For this function class we obtain an inclusion result, Fekete-Szegö inequality coefficient bounds for bi-univalent functions. 1 Introduction Let U r = {z C : z < r} r > 0) let U = U 1 denote the unit disk. Let A be the class of all analytic functions f in U of the form: f = z + a n z n, z U. 1) n=2 Further, by S we shall denote the class of all functions in A which are { univalent} in U. It is known see 6]) that if f S, then fu) contains the disk w < 1 4. Here 1 4 is the best possible constant known as the Koebe constant for S. Thus every univalent function f has an inverse f 1 defined on some disk containing the disk { w < 4} 1 satisfying: f 1 f) = z, z U ff 1 w)) = w, w < r 0 f), r 0 f) 1 4, Key Words: Analytic functions, Fekete-Szegö inequality, bi-univalent functions Mathematics Subject Classification: 30C45. Received: 30 April, Revised: 20 May, Accepted: 29 June,
2 MEANS 268 where f 1 w) = w a 2 w 2 + 2a 2 2 a 3 )w 3 5a 3 2 5a 2 a 3 + a 4 )w ) We denote by S the class of analytic functions which are starlike in U. Let f A α, β R. We define the following function: F = f 1 α zf ) α] 1 β 1 α)f + αzf ] β, α, β R. 3) Remark 1. It is easy to observe that for specific values of β, the function F reduces to some generalised means. If β = 0 we obtain generalised geometric means, if β = 1 we obtain generalised arithmetic means if β = 1 we obtain generalised harmonic means of functions f zf. Definition 1. A function f A is said to be in the class H α,β, α, β R, if the function F defined by 3) is starlike, that is R { 1 β) 1 α) zf + α 1 + zf )] + β zf } + αz 2 f > 0, z U. 4) f f 1 α)f + αzf In order to prove our main results we will need the following lemmas. Lemma 1. 9, p.24] Let q Q, with q0) = a, let p = a + a n z n + be analytic in U with p a n 1. If p is not subordinate to q then there exist z 0 = r 0 e iθ0 U ζ 0 U \ Eq) m n 1 for which pu r0 ) qu) : 1. pz 0 ) = qζ 0 ), 2. z 0 p z 0 ) = mζ 0 q ζ 0 ), 3. R z 0p z 0 ) p z 0 ) + 1 mr ζ0 q ζ 0 ) q ζ 0 ) ] + 1. Denote by P the class of analytic functions p normalized by p0) = 1 having positive real part in U. Lemma 2. 6] Let p P be of the form p = 1 + p 1 z + p 2 z , z U. Then the following estimates hold p n 2, n = 1, 2,.... Lemma 3. 4] If p P is of the form p = 1 + p 1 z + p 2 z , z U. Then 4v + 2, v 0, p2 vp 2 1 2, 0 v 1, 4v 2, v 1.
3 MEANS 269 When v < 0 or v > 1, the equality holds if only if p 1 = 1 + z or one of 1 z its rotations. If 0 < v < 1 then the equality holds if only if p 1 = 1 + z2 1 z 2 or one of its rotations. If v = 0, the equality holds if only if 1 p 1 = ) 1 + z 1 2 λ 1 z ) 1 z 2 λ, λ 0, 1] 1 + z or one of its rotations. If v = 1, the equality holds if only if p 1 is the reciprocal of one of the functions such that the equality holds in the case of v = 0. 2 Inclusion result In this section we show that the new class H α,β is a subclass of the class of starlike functions. Theorem 1. Let α, β R such that αβ1 α) 0. Then H α,β S S. Proof. Let f be in the class H α,β let p = zf f. Then from 4) we obtain that f H α,β if only if { R α1 β) zp p + αβ zp } > 0. 5) 1 α + αp Let q = 1 + z 1 z = 1 + q 1z +. 6) Then = qd) = {w : Rw > 0}, q0) = 1, Eq) = {1} q Q. To prove that f S it is enough to show that { R α1 β) zp p + αβ zp } > 0 p q. 1 α + αp Suppose that p q.then, from Lemma 1,there exist a point z 0 U a point ζ 0 U \ {1} such that pz 0 ) = qζ 0 ) Rp > 0 for all z U z0. This implies that Rpz 0 ) = 0, therefore we can choose pz 0 ) of the form pz 0 ) := ix, where x is a real number. Due to symmetry, it is sufficient to consider only the case where x > 0. We have ζ 0 = q 1 pz 0 )) = pz 0) 1 pz 0 ) + 1,
4 MEANS 270 then z 0 p z 0 ) = mζ 0 q ζ 0 ) = mx 2 + 1) := y, where y < 0. Thus, we obtain: R α1 β) z 0p ] z 0 ) z 0 p ] z 0 ) + R αβ = pz 0 ) 1 α + αpz 0 ) = R α1 β) y ] ] αβy y αβ1 α)] + R = 0 + ix 1 α + αix 1 α + αix 2 0. This contradicts the hypothesis of the theorem, therefore p q the proof of Theorem 1 is complete. 3 Fekete-Szegö problem In 1933 M. Fekete G. Szegö obtained sharp upper bounds for a 3 µa 2 2 for f S µ real number. For this reason, the determination of sharp upper bounds for the non-linear functional a 3 µa 2 2 for any compact family F of functions f A is popularly known as the Fekete-Szegö problem for F. For different subclasses of S, the Fekete-Szegö problem has been investigated by many authors see 2], 4], 11]). In this section we will solve the Fekete-Szegö problem for the class H α,β, where α β are positive real numbers. Theorem 2. Let α, β, µ be positive real numbers. If the function f given by 1) belongs to the class H α,β, then 4µ 2α 1)1 + αβ) + α + 1)5 + α) +, µ σ 1 + α) 2 1, 1 + 2α)1 + α) 2 a 3 µa 2 1 2, σ 1 µ σ 2, 1 + 2α where 4µ 2α 1)1 + αβ) + α + 1)3 α), µ σ 1 + α) α)1 + α) 2 σ 1 = 1 + 3α αβ + α2 β, σ 2 = 2 + 5α + α2 αβ + α 2 β α) α) Proof. Let f be in the class H α, β let p P. From 4) we obtain { 1 β) 1 α) zf f + α 1 + zf )] + β zf } + αz 2 f = p. f 1 α)f + αzf Since f has the Taylor series expansion 1) p = 1+p 1 z+p 2 z , z U, we have α)a 2 z α)a α αβ + α 2 β)a 2 2] z = 7) = 1 + p 1 z + p 2 z
5 MEANS 271 Therefore, equating the coefficients of z 2 z 3 in 7), we obtain a 2 = p α, a 1 3 = p α αβ + α2 β)p 2 ] α 1 + α) 2. So, we have where v = a 3 µa 2 2 = 1 p2 vp 2 ) 1, α) α) 1 + α) 2 µ 1 + 3α αβ + α2 β 1 + α) 2. 8) Now, our result follows as an application of Lemma 3. 4 Subclass of bi-univalent function A function f A is said to be bi-univalent in U if both f f 1 are univalent in U. Let σ be the class of all functions f S such that the inverse function f 1 has an univalent analytic continuation to { w < 1}. The class σ, called the class of bi-univalent functions, was introduced by Levin 7] who showed that a 2 < Branan Clunie 3] conjectured that a 2 2. On the other h, Netanyahu 10] showed that max a 2 = 4. Several authors have f σ 3 studied similar problems in this direction see 1] 5], 8], 12], 13]). We notice that the class σ is not empty. For example, the following functions are members of σ: z, z 1 z, log1 z), 1 2 log 1 + z 1 z. However, the Koebe function is not a member of σ. Other examples of univalent functions that are not in the class σ are z z2 2, z 1 z 2. In the sequel we assume that ϕ is an analytic function with positive real part in the unit disk U, satisfying ϕ0) = 1, ϕ 0) > 0 such that ϕu) is symmetric with respect to the real axis. Assume also that: ϕ = 1 + B 1 z + B 2 z , B 1 > 0. 9)
6 MEANS 272 Definition 2. A function f A is said to be in the class H α,β ϕ), α 0, 1], β 0, if f σ satisfies the following conditions: 1 β) 1 α) zf f + α 1 + zf )] + β zf + αz 2 f f 1 α)f + αzf ϕ, 1 β) )] 1 α) wg w) + α 1 + wg w) + β wg w) + αw 2 g w) gw) g w) 1 α)gw) + αwg w) ϕw), where g is the extension of f 1 to U. Theorem 3. If f H α,β ϕ) is in A then a 2 τ B 1 B1 1 + α) + αβ1 α)]b 2 1 B 2 B 1 )1 + α) 2, 10) ] 1 a 3 B α + αβ1 α) + B 2 B α)1 + α) 1 + α. 11) Proof. Let f H α,β ϕ) g = f 1. Then there exist two analytic functions u, v : U U with u0) = v0) = 0 such that: 1 β) 1 α) zf + α 1 + zf )] + β zf + αz 2 f = ϕu) f f 1 α)f + αzf )] 1 β) 1 α) wg w) + α 1 + wg w) + β w w) + αw 2 g w) gw) g w) 1 α)gw) + αwg w) = ϕvw)). 12) Define the functions p q by p = 1 + u 1 u = 1 + p1z + p2z2 +..., q = 1 + v 1 v = 1 + q1z + q2z or equivalently, u = p 1 p + 1 = 1 2 ) ] p 1 z + p 2 p2 1 2 z2 +..., 13) v = q 1 q + 1 = 1 ) ] q 1 z + q 2 q z )
7 MEANS 273 We observe that p, q P, in view of Lemma 2, we have that p n 2 q n 2, for n 1. Further, using 13) 14) together with 9), it is evident that ϕu) = B 1p 1 z B 1 p p2 1 ) + 1 ] 4 B 2p 2 1 z ) ϕv) = B 1q 1 z + 2 B 1 q 2 1 ) 2 q ] 4 B 2q1 2 z ) Therefore, in view of 12), 15) 16) we have 1 β) 1 α) zf f + α 1 + zf )] f + β zf + αz 2 f 1 α)f + αzf 1 β) = B 1p 1 z + 2 B 1 p 2 1 ) 2 p ) 4 B 2p 2 1 z , 17) )] 1 α) wg w) + α 1 + wg w) gw) g + β wg w) + αw 2 g w) w) 1 α)gw) + αwg w) = B 1q 1 w + 2 B 1 q 2 1 ) 2 q ) 4 B 2q1 2 w ) Since f σ has the Taylor series expansion 1) g = f 1 the series expansion 2), we have 1 β) 1 α) zf f + α 1 + zf )] f + β zf + αz 2 f 1 α)f + αzf = α)a 2 z α)a α αβ + α 2 β)a 2 2] z , 19) 1 β) )] 1 α) wg w) + α 1 + wg w) gw) g + β wg w) + αw 2 g w) w) 1 α)gw) + αwg w) = α)a 2w α)a α αβ + α 2 β)a 3 2a 2 2) ] w )
8 MEANS 274 Equating the coefficients in 17), 19) 18), 20), we obtain 1 + α)a 2 = 1 2 B1p1, α)a α αβ + α 2 β)a 2 2 = 1 ) 2 B1 p 2 p B2p2 1, 1 + α)a 2 = 1 2 B1q1, α)a 3 2a 2 2) 1 + 3α αβ + α 2 β)a 2 2 = 1 ) 2 B1 q 2 q B2q ) From the first the third equation of the system 21) it follows that a 2 2 = p 1 = q 1, 22) ) 2 B1 p 1 τ. 23) 41 + γ) Now, 22), 23) the next two equations of the system 21) lead to a 2 2 = B 3 1p 2 + q 2 ) 41 + α) + αβ1 α)]b 2 1 4B 2 B 1 )1 + α) 2. 24) Thus, in view of Lemma 2, we obtain the desired estimation of a 2. From the third the fourth equation of 21), we obtain a 3 = 1 2 B 1p α + αβ1 α) α)1 + α) α αβ1 α) α)1 + α) p2 1B 2 B 1 ) 1 + α, which yields to the estimate given by 11) so the proof of Theorem 3 is completed. References 1] R. M. Ali, S. K. Lee, V. Ravichran, S. Supramanian, Coefficient estimates for bi-univalent Ma-Minda starlike convex functions, Appl. Math. Lett ), ] D. Bansal, Fekete-Szegö problem for a new class of analytic functions, Int. J. Math. Mathematical Sciences ), article ID: , 5 pages.
9 MEANS 275 3] D. A. Branan, J. G. Clunie, W. E. Kirwan, Coefficient estimates for a class of starlike functions, Canad. J. Math ), ] M. Fekete, G. Szegö, Eine Bemerkung über ungerade schlichte Functionen, J. London Math. Soc ), ] S. P. Goyal, P. Goswami, Estimate for initial Maclaurin coefficients of biunivalent functions for a class defined by fractional derivatives, J. Egyptian Math. Soc ), issue 3, ] A. W. Goodman, Univalent functions, Polygonal Publishing House, Washington, New Jersey, ] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc ), ] X.-F. Li, A.-P. Wang, Two new subclasses of bi-univalent functions, Int. Math. Forum no. 30, 72012), ] S.S. Miller, P.T. Mocanu, Differential Subordinations: Theory Applications, Dekker, New York, ] E. Netanyahu, The minimal distance of the image boundary from the origin the second coefficient of a univalent function in z < 1, Arch. Ration. Mech. Anal ), ] H. M. Srivastava, A. K. Mishra, M. K. Das, The Fekete-Szegö problem for a subclass of close-to-convex functions, Complex Variables, Theory Appl ), ] H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic bi-univalent functions, Appl. Math. Lett ), ] Q.-H. Xu, Y.-C. Gui, H.M. Srivastava, Coefficient estimates for a certain subclass of analytic bi-univalent functions, Appl. Math. Lett ), Andreea-Elena TUDOR, Department of Mathematics, Transilvania University of Braşov, Str.Iuliu Maniu 50, , Brasov, Romania. tudor reea elena@yahoo.com Dorina RĂDUCANU, Department of Mathematics, Transilvania University of Braşov, Str.Iuliu Maniu 50, , Brasov, Romania. draducanu@unitbv.ro
10 MEANS 276
Subclasses 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 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 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 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 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 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 informationCOEFFICIENT 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 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 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 informationAN EXTENSION OF THE REGION OF VARIABILITY OF A SUBCLASS OF UNIVALENT FUNCTIONS
AN EXTENSION OF THE REGION OF VARIABILITY OF A SUBCLASS OF UNIVALENT FUNCTIONS SUKHWINDER SINGH SUSHMA GUPTA AND SUKHJIT SINGH Department of Applied Sciences Department of Mathematics B.B.S.B. Engineering
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 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 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 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 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 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 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 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 informationOn close-to-convex functions satisfying a differential inequality
Stud. Univ. Babeş-Bolyai Math. 60(2015), No. 4, 561 565 On close-to-convex functions satisfying a differential inequality Sukhwinder Singh Billing Abstract. Let C α(β) denote the class of normalized functions
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 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 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 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 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 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 informationOn sandwich theorems for p-valent functions involving a new generalized differential operator
Stud. Univ. Babeş-Bolyai Math. 60(015), No. 3, 395 40 On sandwich theorems for p-valent functions involving a new generalized differential operator T. Al-Hawary, B.A. Frasin and M. Darus Abstract. A new
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 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 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 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 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 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 informationA NOTE ON UNIVALENT FUNCTIONS WITH FINITELY MANY COEFFICIENTS. Abstract
A NOTE ON UNIVALENT FUNCTIONS WITH FINITELY MANY COEFFICIENTS M. Darus, R.W. Ibrahim Abstract The main object of this article is to introduce sufficient conditions of univalency for a class of analytic
More informationCoefficient Bounds for Certain Subclasses of Analytic Function Involving Hadamard Products
Mathematica Aeterna, Vol. 4, 2014, no. 4, 403-409 Coefficient Bounds for Certain Subclasses of Analytic Function Involving Hadamard Products V.G. Shanthi Department of Mathematics S.D.N.B. Vaishnav College
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 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 informationA SUBORDINATION THEOREM WITH APPLICATIONS TO ANALYTIC FUNCTIONS
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 3(2011, Pages 1-8. A SUBORDINATION THEOREM WITH APPLICATIONS TO ANALYTIC FUNCTIONS (COMMUNICATED
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 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 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 informationarxiv: v1 [math.cv] 28 Mar 2017
On third Hankel determinants for subclasses of analytic functions and close-to-convex harmonic mappings arxiv:703.09485v math.cv] 28 Mar 207 Yong Sun, Zhi-Gang Wang 2 and Antti Rasila 3 School of Science,
More informationFABER POLYNOMIAL COEFFICIENTS FOR GENERALIZED BI SUBORDINATE FUNCTIONS OF COMPLEX ORDER
Journal of Mathematical Inequalities Volume, Number 3 (08), 645 653 doi:0.753/jmi-08--49 FABER POLYNOMIAL COEFFICIENTS FOR GENERALIZED BI SUBORDINATE FUNCTIONS OF COMPLEX ORDER ERHAN DENIZ, JAY M. JAHANGIRI,
More informationDifferential subordination related to conic sections
J. Math. Anal. Appl. 317 006 650 658 www.elsevier.com/locate/jmaa Differential subordination related to conic sections Stanisława Kanas Department of Mathematics, Rzeszów University of Technology, W. Pola,
More informationSANDWICH-TYPE THEOREMS FOR A CLASS OF INTEGRAL OPERATORS ASSOCIATED WITH MEROMORPHIC FUNCTIONS
East Asian Mathematical Journal Vol. 28 (2012), No. 3, pp. 321 332 SANDWICH-TYPE THEOREMS FOR A CLASS OF INTEGRAL OPERATORS ASSOCIATED WITH MEROMORPHIC FUNCTIONS Nak Eun Cho Abstract. The purpose of the
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 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 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 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 informationCoefficients estimates of some subclasses of analytic functions related with conic domain
DOI: 10.2478/auom-2013-0031 An. Şt. Univ. Ovidius Constanţa Vol. 212),2013, 181 188 Coefficients estimates of some subclasses of analytic functions related with conic domain Abstract In this paper, the
More informationGrowth and distortion theorem for the Janowski alpha-spirallike functions in the unit disc
Stud. Univ. Babeş-Bolyai Math. 57(01), No., 55 59 Growth and distortion theorem for the Janowski alpha-spirallike functions in the unit disc Yaşar Polato glu Abstract. Let A be the class of all analytic
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 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 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 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 informationSufficient conditions for certain subclasses of meromorphic p-valent functions
Bol. Soc. Paran. Mat. (3s.) v. 33 (015): 9 16. c SPM ISSN-175-1188 on line ISSN-0037871 in ress SPM: www.sm.uem.br/bsm doi:10.569/bsm.v33i.1919 Sufficient conditions for certain subclasses of meromorhic
More informationdenote the subclass of the functions f H of the form H of the form
Scholars Journal of Engineering and Technology (SJET) Sch. J. Eng. Tech., 05; 3(4C):55-59 Scholars Academic and Scientific Publisher (An International Publisher for Academic and Scientific Resources) www.saspublisher.com
More informationSubclasses of starlike functions associated with some hyperbola 1
General Mathematics Vol. 14, No. 2 2006, 31 42 Subclasses of starlike functions associated with some hyperbola 1 Mugur Acu Abstract In this paper we define some subclasses of starlike functions associated
More informationBIII/. Malaysinn Math. Sc. Soc. (Second Series) 26 (2003) Coefficients of the Inverse of Strongly Starlike Functions. ROSlHAN M.
BULLETIN of the MALAYSIAN MATHEMATICAL SCIENCES SOCIETY BIII/. Malaysinn Math. Sc. Soc. (Second Series) 26 (2003) 63-71 Coefficients of the Inverse of Strongly Starlike Functions ROSlHAN M. ALI School
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 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 informationUniformly convex functions II
ANNALES POLONICI MATHEMATICI LVIII. (199 Uniformly convex functions II by Wancang Ma and David Minda (Cincinnati, Ohio Abstract. Recently, A. W. Goodman introduced the class UCV of normalized uniformly
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 informationON CERTAIN SUBCLASSES OF UNIVALENT FUNCTIONS AND RADIUS PROPERTIES
ON CERTAIN SUBCLASSES OF UNIVALENT FUNCTIONS AND RADIUS PROPERTIES M. OBRADOVIĆ and S. PONNUSAMY Let S denote the class of normalied univalent functions f in the unit disk. One of the problems addressed
More informationDIFFERENTIAL SUBORDINATION RESULTS FOR NEW CLASSES OF THE FAMILY E(Φ, Ψ)
DIFFERENTIAL SUBORDINATION RESULTS FOR NEW CLASSES OF THE FAMILY E(Φ, Ψ) Received: 05 July, 2008 RABHA W. IBRAHIM AND MASLINA DARUS School of Mathematical Sciences Faculty of Science and Technology Universiti
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 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 informationCERTAIN DIFFERENTIAL SUBORDINATIONS USING A GENERALIZED SĂLĂGEAN OPERATOR AND RUSCHEWEYH OPERATOR. Alina Alb Lupaş
CERTAIN DIFFERENTIAL SUBORDINATIONS USING A GENERALIZED SĂLĂGEAN OPERATOR AND RUSCHEWEYH OPERATOR Alina Alb Lupaş Dedicated to Prof. H.M. Srivastava for the 70th anniversary Abstract In the present paper
More informationMULTIVALENTLY MEROMORPHIC FUNCTIONS ASSOCIATED WITH CONVOLUTION STRUCTURE. Kaliyapan Vijaya, Gangadharan Murugusundaramoorthy and Perumal Kathiravan
Acta Universitatis Apulensis ISSN: 1582-5329 No. 30/2012 pp. 247-263 MULTIVALENTLY MEROMORPHIC FUNCTIONS ASSOCIATED WITH CONVOLUTION STRUCTURE Kaliyapan Vijaya, Gangadharan Murugusundaramoorthy and Perumal
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 informationApplied Mathematics Letters
Applied Mathematics Letters 3 (00) 777 78 Contents lists availale at ScienceDirect Applied Mathematics Letters journal homepage: wwwelseviercom/locate/aml Fekete Szegö prolem for starlike convex functions
More informationn=2 AMS Subject Classification: 30C45. Keywords and phrases: Starlike functions, close-to-convex functions, differential subordination.
MATEMATIQKI VESNIK 58 (2006), 119 124 UDK 517.547 originalni nauqni rad research paper ON CETAIN NEW SUBCLASS OF CLOSE-TO-CONVEX FUNCTIONS Zhi-Gang Wang, Chun-Yi Gao and Shao-Mou Yuan Abstract. In the
More informationDIFFERENTIAL SANDWICH THEOREMS FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING A LINEAR OPERATOR. 1. Introduction
Acta Math. Univ. Comenianae Vol. LXXVI, 2(2007), pp. 287 294 287 DIFFERENTIAL SANDWICH THEOREMS FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING A LINEAR OPERATOR T. N. SHAMMUGAM, C. RAMACHANDRAN, M.
More informationBanach Journal of Mathematical Analysis ISSN: (electronic)
Banach J. Math. Anal. (008), no., 16 Banach Journal of Mathematical Analysis ISSN: 1735-8787 (electronic) http://www.math-analysis.org GENEALIZATION OF SǍLǍGEAN OPEATO FO CETAIN ANALYTIC FUNCTIONS ALAWIAH
More informationj(z) > + FZ f(z) z + oz f(z) 1-.F < 1-.F zf (z) } 1 E (z 6 U,F 1). (1.3) >/(z e u) ANGULAR ESTIMATIONS OF CERTAIN INTEGRAL OPERATORS
Internat. J. Math. & Math. Sci. VOL. 1 NO. (1998) 369374 369 ANGULAR ESTIMATIONS OF CERTAIN INTEGRAL OPERATORS NAK EUN CHO, IN HWA KIM JI A KIM Department of Applied Mathematics Pukyong National University
More informationA general coefficient inequality 1
General Mathematics Vol. 17, No. 3 (2009), 99 104 A general coefficient inequality 1 Sukhwinder Singh, Sushma Gupta and Sukhjit Singh Abstract In the present note, we obtain a general coefficient inequality
More informationSOME CRITERIA FOR STRONGLY STARLIKE MULTIVALENT FUNCTIONS
Bulletin of the Institute of Mathematics Academia Sinica (New Series) Vol. 7 (01), No. 3, pp. 43-436 SOME CRITERIA FOR STRONGLY STARLIKE MULTIVALENT FUNCTIONS DINGGONG YANG 1 AND NENG XU,b 1 Department
More informationResearch Article New Classes of Analytic Functions Involving Generalized Noor Integral Operator
Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008, Article ID 390435, 14 pages doi:10.1155/2008/390435 Research Article New Classes of Analytic Functions Involving Generalized
More informationDIFFERENTIAL SUBORDINATION FOR MEROMORPHIC MULTIVALENT QUASI-CONVEX FUNCTIONS. Maslina Darus and Imran Faisal. 1. Introduction and preliminaries
FACTA UNIVERSITATIS (NIŠ) SER. MATH. INFORM. 26 (2011), 1 7 DIFFERENTIAL SUBORDINATION FOR MEROMORPHIC MULTIVALENT QUASI-CONVEX FUNCTIONS Maslina Darus and Imran Faisal Abstract. An attempt has been made
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 informationThe Order of Starlikeness of New p-valent Meromorphic Functions
Int. Journal of Math. Analysis, Vol. 6, 2012, no. 27, 1329-1340 The Order of Starlikeness of New p-valent Meromorphic Functions Aabed Mohammed and Maslina Darus School of Mathematical Sciences Faculty
More informationDIFFERENTIAL SANDWICH THEOREMS FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING A LINEAR OPERATOR. 1. Introduction
DIFFERENTIAL SANDWICH THEOREMS FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING A LINEAR OPERATOR T. N. SHAMMUGAM, C. RAMACHANDRAN, M. DARUS S. SIVASUBRAMANIAN Abstract. By making use of the familiar
More informationOn the improvement of Mocanu s conditions
Nunokawa et al. Journal of Inequalities Applications 13, 13:46 http://www.journalofinequalitiesapplications.com/content/13/1/46 R E S E A R C H Open Access On the improvement of Mocanu s conditions M Nunokawa
More informationDIFFERENTIAL SUBORDINATION ASSOCIATED WITH NEW GENERALIZED DERIVATIVE OPERATOR
ROMAI J., v.12, no.1(2016), 77 89 DIFFERENTIAL SUBORDINATION ASSOCIATED WITH NEW GENERALIZED DERIVATIVE OPERATOR Anessa Oshah, Maslina Darus School of Mathematical Sciences, Faculty of Science and Technology,
More informationSome Geometric Properties of a Certain Subclass of Univalent Functions Defined by Differential Subordination Property
Gen. Math. Notes Vol. 20 No. 2 February 2014 pp. 79-94 SSN 2219-7184; Copyright CSRS Publication 2014 www.i-csrs.org Available free online at http://www.geman.in Some Geometric Properties of a Certain
More informationINTEGRAL MEANS OF UNIVALENT SOLUTION FOR FRACTIONAL EQUATION IN COMPLEX PLANE. Rabha W. Ibrahim and Maslina Darus
Acta Universitatis Apulensis ISSN: 1582-5329 No. 23/21 pp. 39-47 INTEGRAL MEANS OF UNIVALENT SOLUTION FOR FRACTIONAL EQUATION IN COMPLEX PLANE Rabha W. Ibrahim and Maslina Darus Abstract. Integral means
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 informationConvolutions of Certain Analytic Functions
Proceedings of the ICM2010 Satellite Conference International Workshop on Harmonic and Quasiconformal Mappings (HQM2010) Editors: D. Minda, S. Ponnusamy, and N. Shanmugalingam J. Analysis Volume 18 (2010),
More informationOn a subclass of n-close to convex functions associated with some hyperbola
General Mathematics Vol. 13, No. 3 (2005), 23 30 On a subclass of n-close to convex functions associated with some hyperbola Mugur Acu Dedicated to Professor Dumitru Acu on his 60th anniversary Abstract
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 informationDifferential Sandwich Theorem for Multivalent Meromorphic Functions associated with the Liu-Srivastava Operator
KYUNGPOOK Math. J. 512011, 217-232 DOI 10.5666/KMJ.2011.51.2.217 Differential Sandwich Theorem for Multivalent Meromorhic Functions associated with the Liu-Srivastava Oerator Rosihan M. Ali, R. Chandrashekar
More informationSubclasses of Analytic Functions with Respect. to Symmetric and Conjugate Points
Theoretical Mathematics & Applications, vol.3, no.3, 2013, 1-11 ISSN: 1792-9687 (print), 1792-9709 (online) Scienpress Ltd, 2013 Subclasses of Analytic Functions with Respect to Symmetric and Conjugate
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 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 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 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 informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics INTEGRAL MEANS INEQUALITIES FOR FRACTIONAL DERIVATIVES OF SOME GENERAL SUBCLASSES OF ANALYTIC FUNCTIONS TADAYUKI SEKINE, KAZUYUKI TSURUMI, SHIGEYOSHI
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 informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics APPLICATIONS OF DIFFERENTIAL SUBORDINATION TO CERTAIN SUBCLASSES OF MEROMORPHICALLY MULTIVALENT FUNCTIONS H.M. SRIVASTAVA AND J. PATEL Department
More informationResearch Article Differential Subordinations of Arithmetic and Geometric Means of Some Functionals Related to a Sector
International Journal of Mathematics and Mathematical Sciences Volume 2011, Article ID 205845, 19 pages doi:10.1155/2011/205845 Research Article Differential Subordinations of Arithmetic and Geometric
More information