Coefficient Bounds for a Certain Class of Analytic and Bi-Univalent Functions
|
|
- Corey Shelton
- 6 years ago
- Views:
Transcription
1 Filomat 9:8 (015), DOI 10.98/FIL S Published by Faculty of Sciences Mathematics, University of Niš, Serbia Available at: Coefficient Bounds for a Certain Class of Analytic Bi-Univalent Functions H. M. Srivastava a, Sevtap Sümer Eker b, Rosihan M. Ali c a Department of Mathematics Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada b Department of Mathematics, Faculty of Science, Dicle University, TR-180 Diyarbakır, Turkey c School of Mathematical Sciences, Universiti Sains Malaysia, USM Penang, Malaysia Abstract. In this paper, we introduce investigate a subclass of analytic bi-univalent functions in the open unit disk U. By using the Faber polynomial expansions, we obtain upper bounds for the coefficients of functions belonging to this analytic bi-univalent function class. ome interesting recent developments involving other subclasses of analytic bi-univalent functions are also briefly mentioned. 1. Introduction Let A denote the class of functions f (z) which are analytic in the open unit disk U = {z : z C z < 1} normalized by the following Taylor-Maclaurin series expansion: f (z) = z a n z n. (1.1) Also let S denote the subclass of functions in A which are univalent in U (see, for details, [8]). It is well known that every function f S has an inverse f 1, which is defined by f 1( f (z) ) = z (z U) f ( f 1 (w) ) = w ( w < r 0 ( f ); r 0 ( f ) 1 ), (1.) Mathematics Subject Classification. Primary 30C45, 30C50; Secondary 30C80 Keywords. Analytic functions; Univalent functions; Faber polynomials; Bi-Univalent functions; Taylor-Maclaurin series expansion; Coefficient bounds coefficient estimates; Taylor-Maclaurin coefficients. Received: 06 November 013; Accepted: 1 April 014 Communicated by Dragan S. Djordjević addresses: harimsri@math.uvic.ca (H. M. Srivastava), sevtaps35@gmail.com (Sevtap Sümer Eker), rosihan@cs.usm.my (Rosihan M. Ali)
2 H. M. Srivastava et al. / Filomat 9:8 (015), according to the Koebe One-Quarter Theorem (see, for example, [8]). In fact, the inverse function f 1 is given by f 1 (w) = w a w ( a a ) 3 w 3 ( 5a 3 5a a 3 a 4 ) w 4. (1.3) A function f A is said to be bi-univalent in U if both f (z) f 1 (z) are univalent in U. Let denote the class of analytic bi-univalent functions in U given by the Taylor-Maclaurin series expansion (1.1). Some examples of functions in the class are presented below: ( ) z 1 z, log(1 z), 1 1 z log, 1 z so on. However, the familiar Koebe function is not a member of the class. Other common examples of functions in S such as z z z 1 z are also not members of the class. For a brief history of functions in the class, see [] (see also [4], [14], [18] [5]). In fact, judging by the remarkable flood of papers on the subject (see, for example, [5 7, 9 1, 15 17, 19 1, 3, 6, 7, 9, 30]), the recent pioneering work of Srivastava et al.[] appears to have revived the study of analytic bi-univalent functions in recent years (see also [3], [13] [4]). The object of the present paper is to introduce a new subclass of the function class use the Faber polynomial expansion techniques to derive bounds for the general Taylor-Maclaurin coefficients a n for the functions in this class. We also obtain estimates for the first two coefficients a a 3 of these functions.. Bounds Derivable by the Faber Polynomial Expansion Techniques We begin by introducing the function class N (α,λ) by means of the following definition. Definition. A function f (z) given by (1.1) is said to be in the class N (α,λ) (0 α < 1; λ 0) if the following conditions are satisfied: f R { f (z) λz f (z) } > α (z U; 0 α < 1; λ 0). (.1) By using the Faber polynomial expansions of functions f A of the form (1.1), the coefficients of its inverse map = f 1 may be expressed as follows (see [1] []; see also [1]): where (w) = f 1 (w) = w K n n 1 = ( n 1)!(n 1)! an 1 1 n K n n 1 (a, a 3,, a n ) w n. (.) (( n 1))!(n 3)! an 3 a 3 ( n 3)!(n 4)! an 4 a 4 [ (( n ))!(n 5)! an 5 a5 ( n )a3] ( n 5)!(n 6)! an 6 [a 6 ( n 5)a 3 a 4 ] a n j V j, j 7
3 H. M. Srivastava et al. / Filomat 9:8 (015), where such expressions as (for example) are to be interpreted symbolically by Γ(1 n) := ( n)( n 1)( n ) ( n N0 := N {0} (N := {1,, 3, }) ) (.3) V j (7 j n) is a homogeneous polynomial in the variables a, a 3,, a n (see, for details, []). In particular, the first three terms of K n are given below: n 1 K 1 = a, K 3 = 3 ( a a ) 3 K 4 3 = 4 ( 5a 3 5a a 3 a 4 ). In general, an expansion of K p n is given by (see, for details, [1]) where K p n = pa n p(p 1) D n p! (p 3)!3! D3 n Z := {0, ±1, ±, } D p n = D p n (a, a 3, ), alternatively, by (see, for details, [8]) D m n (a 1, a,, a n ) = ( ) m! a µ 1 µ 1! µ n! 1 aµ n n, p! (p n)!n! Dn n (p Z) where a 1 = 1 the sum is taken over all nonnegative integers µ 1,, µ n satisfying the following conditions: µ 1 µ µ n = m It is clear that µ 1 µ nµ n = n. D n n(a 1, a,, a n ) = a n 1. Our first main result is given by Theorem 1 below. Theorem 1. Let f given by (1.1) be in the class N α,λ (0 α < 1 λ 0). If a k = 0 for k n 1, then a n n[1 λ(n 1)] (n N \ {1, }). (.4) Proof. For analytic functions f of the form (1.1), we have f (z) λz f (z) = 1 [1 λ(n 1)]na n z n 1 (.5)
4 , for its inverse map = f 1, it is seen that (w) λw (w) = 1 = 1 H. M. Srivastava et al. / Filomat 9:8 (015), [1 λ(n 1)]nb n w n 1 [1 λ(n 1)]K n n 1 (a, a 3,, a n ) w n 1. (.6) On the other h, since f N α,λ functions p(z) = 1 c n z n = f 1 N α,λ, by definition, there exist two positive real-part q(w) = 1 d n w n, where so that R ( p(z) ) > 0 R ( q(w) ) > 0 (z, w U), f (z) λz f (z) = α (1 α)p(z) = 1 (1 α) Kn 1 (c 1, c,, c n ) z n (.7) (w) λw (w) = α (1 α)q(w) = 1 (1 α) Kn 1 (d 1, d,, d n ) w n. (.8) Thus, upon comparing the corresponding coefficients in (.5) (.7), we get [1 λ(n 1)]na n = (1 α)k 1 n 1 (c 1, c,, c n 1 ). (.9) Similarly, by using (.6) (.8), we find that so [1 λ(n 1)]K n n 1 (a 1, a,, a n ) = (1 α)k 1 n 1 (d 1, d,, d n 1 ). (.10) We note that, for a k = 0 ( k n 1), we have b n = a n [1 λ(n 1)]na n = (1 α)c n 1 (.11) [1 λ(n 1)]na n = (1 α)d n 1. (.1)
5 H. M. Srivastava et al. / Filomat 9:8 (015), Thus, according to the Carathéodory Lemma (see [8]), we also observe that c n d n (n N). Now, taking the moduli in (.11) (.1) applying the Carathéodory Lemma, we obtain a n (1 α) c n 1 n[1 λ(n 1)] = (1 α) d n 1 n[1 λ(n 1)] n[1 λ(n 1)], (.13) which evidently completes the proof of Theorem Estimates for the Initial Coefficients a a 3 In this section, we choose to relax the coefficient restrictions imposed in Theorem 1 derive the resulting estimates for the initial coefficients a a 3 of functions f N α,λ given by the Taylor-Maclaurin series expansion (1.1). We first state the following theorem. Theorem. Let f given by (1.1) be in the class N α,λ (0 α < 1 λ 0). Then a 1 λ λ, 0 α < 3(1 λ) 3(1 λ) 1 α 1 λ, 1 λ λ α < 1 3(1 λ) (3.1) a 3 3(1 λ). (3.) Proof. If we set n = by n = 3 in (.9) (.10), respectively, we obtain (1 λ)a = (1 α)c 1, (3.3) 3(1 λ)a 3 = (1 α)c, (1 λ)a = (1 α)d 1 (3.5) (3.4) 3(1 λ)(a a 3) = (1 α)d. (3.6) Upon dividing both sides of (3.3) or (3.5) by (1λ), if we take their moduli apply the Carathéodory Lemma, we find that a (1 α) c 1 (1 λ) = (1 α) d 1 (1 λ) Now, by adding (3.4) to (3.6), we have 1 α 1 λ. (3.7) 6(1 λ)a = (1 α)(c d ), (3.8)
6 H. M. Srivastava et al. / Filomat 9:8 (015), that is, a = (1 α)(c d ). 6(1 λ) (3.9) Another application of the Carathéodory Lemma followed by taking the square roots in this last equation (3.9) yields a 3(1 λ), (3.10) which proves the first assertion (3.1) of Theorem. Next, for 1 λ λ 3(1 λ) α < 1, we note that 1 α 1 λ 3(1 λ). (3.11) Thus, upon dividing both sides of (3.4) by 3(1 λ), if we take the modulus of each side apply the Carathéodory Lemma once again, we get a 3 3(1 λ), (3.1) which completes the proof of the second assertion (3.) of Theorem. References [1] H. Airault A. Bouali, Differential calculus on the Faber polynomials, Bull. Sci. Math. 130 (006), 179. [] H. Airault J.-G. Ren, An algebra of differential operators generating functions on the set of univalent functions, Bull. Sci. Math. 16 (00), [3] R. M. Ali, S. K. Lee, V. Ravichran S. Supramaniam, Coefficient estimates for bi-univalent Ma-Minda starlike convex functions, Appl. Math. Lett. 5 (01), [4] D. A. Brannan T. S. Taha, On some classes of bi-univalent functions, in Mathematical Analysis Its Applications (S. M. Mazhar, A. Hamoui N. S. Faour, Editors) (Kuwait; February 18 1, 1985), KFAS Proceedings Series, Vol. 3, Pergamon Press (Elsevier Science Limited), Oxford, 1988, pp ; see also Studia Univ. Babeş-Bolyai Math. 31 () (1986) [5] S. Bulut, Coefficient estimates for a class of analytic bi-univalent functions, Novi Sad J. Math. 43 () (013), [6] M. Çağlar, H. Orhan N. Yağmur, Coefficient bounds for new subclasses of bi-univalent functions, Filomat 7 (013), [7] E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal. (013), [8] P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, B 59, Springer-Verlag, New York, Berlin, Heidelberg Tokyo, [9] B. A. Frasin M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 4 (011), [10] S. P. Goyal P.Goswami, Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, J. Egyptian Math. Soc. 0 (01), [11] T. Hayami S. Owa, Coefficient bounds for bi-univalent functions, Pan Amer. Math. J. (4) (01), [1] J. M. Jahangiri S. G. Hamidi, Coefficient estimates for certain classes of bi-univalent functions, Internat. J. Math. Math. Sci. 013 (013), Article ID , 1 4. [13] A. W. Kedzierawski, Some remarks on bi-univalent functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 39 (1985), [14] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), [15] X.-F. Li A.-P. Wang, Two new subclasses of bi-univalent functions, Internat. Math. Forum 7 (01), [16] N. Magesh J. Yamini, Coefficient bounds for certain subclasses of bi-univalent functions, Internat. Math. Forum 8 (013), [17] G. Murugusundaramoorthy, N. Magesh V. Prameela, Coefficient bounds for certain subclasses of bi-univalent functions, Abstr. Appl. Anal. 013 (013), Article ID , 1 3. [18] E. Netanyahu, The minimal distance of the image boundary from the origin the second coefficient of a univalent function in z < 1, Arch. Rational Mech. Anal. 3 (1969),
7 H. M. Srivastava et al. / Filomat 9:8 (015), [19] Z.-G. Peng Q.-Q. Han, On the coefficients of several classes of bi-univalent functions, Acta Math. Sci. Ser. B Engl. Ed. 34 (014), [0] H. M. Srivastava, Some inequalities other results associated with certain subclasses of univalent bi-univalent analytic functions, in: Nonlinear Analysis: Stability, Approximation, Inequalities (Panos M. Pardalos, Po G. Georgiev Hari M. Srivastava, Editors.), Springer Series on Optimization Its Applications, Vol. 68, Springer-Verlag, Berlin, Heidelberg New York, 01, pp [1] H. M. Srivastava, S. Bulut, M. Çağlar N. Yağmur, Coefficient estimates for a general subclass of analytic bi-univalent functions, Filomat 7 (013), [] H. M. Srivastava, A. K. Mishra P. Gochhayat, Certain subclasses of analytic bi-univalent functions, Appl. Math. Lett. 3 (010), [3] H. M. Srivastava, G. Murugusundaramoorthy N. Magesh, Certain subclasses of bi-univalent functions associated with the Hohlov operator, Global J. Math. Anal. 1 () (013), [4] D. Styer J. Wright, Result on bi-univalent functions, Proc. Amer. Math. Soc. 8 (1981), [5] T. S. Taha, Topics in Univalent Function Theory, Ph.D. Thesis, University of London, [6] D.-L. Tan, Coefficient estimates for bi-univalent functions, Chinese Ann. Math. Ser. A 5 (1984), [7] H. Tang, G.-T. Deng S.-H. Li, Coefficient estimates for new subclasses of Ma-Minda bi-univalent functions, J. Inequal. Appl. 013 (013), Article ID 317, [8] P. G. Todorov, On the Faber polynomials of the univalent functions of class, J. Math. Anal. Appl. 16 (1991), [9] Q.-H. Xu, Y.-C. Gui H. M. Srivastava, Coefficient estimates for a certain subclass of analytic bi-univalent functions, Appl. Math. Lett. 5 (01), [30] 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. 18 (01),
Initial 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationConvolution Properties for Certain Meromorphically Multivalent Functions
Filomat 31:1 (2017), 113 123 DOI 10.2298/FIL1701113L Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: htt://www.mf.ni.ac.rs/filomat Convolution Proerties for Certain
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 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 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 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 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 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 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 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 informationA NOVEL SUBCLASS OF UNIVALENT FUNCTIONS INVOLVING OPERATORS OF FRACTIONAL CALCULUS P.N. Kamble 1, M.G. Shrigan 2, H.M.
International Journal of Applied Mathematics Volume 30 No. 6 2017, 501-514 ISSN: 1311-1728 printed version; ISSN: 1314-8060 on-line version doi: http://dx.doi.org/10.12732/ijam.v30i6.4 A NOVEL SUBCLASS
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 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 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 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 informationRosihan M. Ali, M. Hussain Khan, V. Ravichandran, and K. G. Subramanian. Let A(p, m) be the class of all p-valent analytic functions f(z) = z p +
Bull Korean Math Soc 43 2006, No 1, pp 179 188 A CLASS OF MULTIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS DEFINED BY CONVOLUTION Rosihan M Ali, M Hussain Khan, V Ravichandran, and K G Subramanian Abstract
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 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 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 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 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 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 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 informationarxiv: v2 [math.cv] 24 Nov 2009
On strongly starlike and convex functions of orderαand typeβ IKKEI HOTTA Division of Mathematics, Graduate School of Information Sciences, Tohoku University, 6-3-09 Aramaki-Aza-Aoba, Aoba-ku, Sendai, Miyagi
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 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 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 informationResearch Article Integral Means Inequalities for Fractional Derivatives of a Unified Subclass of Prestarlike Functions with Negative Coefficients
Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 27, Article ID 97135, 9 pages doi:1.1155/27/97135 Research Article Integral Means Inequalities for Fractional Derivatives
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 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 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 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 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 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 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 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 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 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 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 informationON SOME LENGTH PROBLEMS FOR ANALYTIC FUNCTIONS
Nunokawa, M. and Sokół, J. Osaka J. Math. 5 (4), 695 77 ON SOME LENGTH PROBLEMS FOR ANALYTIC FUNCTIONS MAMORU NUNOKAWA and JANUSZ SOKÓŁ (Received December 6, ) Let A be the class of functions Abstract
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 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 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 informationAn Application of Wilf's Subordinating Factor Sequence on Certain Subclasses of Analytic Functions
International Journal of Applied Engineering Research ISS 0973-4562 Volume 3 umber 6 (208 pp. 2494-2500 An Application of Wilf's Subordinating Factor Sequence on Certain Subclasses of Analytic Functions
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 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 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 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 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 informationA subclass of analytic functions
Stud. Univ. Babeş-Bolyai Math. 57(2012), No. 2, 277 282 A subclass of analytic functions Andreea-Elena Tudor Abstract. In the present paper, by means of Carlson-Shaffer operator and a multiplier transformation,
More informationSOME APPLICATIONS OF SALAGEAN INTEGRAL OPERATOR. Let A denote the class of functions of the form: f(z) = z + a k z k (1.1)
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LV, Number 1, March 2010 SOME APPLICATIONS OF SALAGEAN INTEGRAL OPERATOR Abstract. In this paper we introduce and study some new subclasses of starlike, convex,
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 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 informationSOME PROPERTIES OF A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY A GENERALIZED SRIVASTAVA-ATTIYA OPERATOR. Nagat. M. Mustafa and Maslina Darus
FACTA UNIVERSITATIS NIŠ) Ser. Math. Inform. Vol. 27 No 3 2012), 309 320 SOME PROPERTIES OF A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY A GENERALIZED SRIVASTAVA-ATTIYA OPERATOR Nagat. M. Mustafa and Maslina
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 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 informationZ bz Z klak --bkl <-- 6 (12) Z bkzk lbl _< 6. Z akzk (ak _> O, n e N {1,2,3,...}) N,,,(e) g A(n) g(z)- z- > (z U) (2 l) f(z)
Internat. J. Math. & Math. Sci. VOL. 19 NO. 4 (1996) 797-800 797 NEIGHBORHOODS OF CERTAIN ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS OSMAN ALTINTAS Department of Mathematics Hacettepe University Beytepe,
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 informationResearch Article A Third-Order Differential Equation and Starlikeness of a Double Integral Operator
Abstract and Applied Analysis Volume 2, Article ID 9235, pages doi:.55/2/9235 Research Article A Third-Order Differential Equation and Starlikeness of a Double Integral Operator Rosihan M. Ali, See Keong
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 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 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 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 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 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 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 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 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 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 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 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 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 informationSubclasses of Analytic Functions. Involving the Hurwitz-Lerch Zeta Function
International Mathematical Forum, Vol. 6, 211, no. 52, 2573-2586 Suclasses of Analytic Functions Involving the Hurwitz-Lerch Zeta Function Shigeyoshi Owa Department of Mathematics Kinki University Higashi-Osaka,
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 informationSubclass Of K Uniformly Starlike Functions Associated With Wright Generalized Hypergeometric Functions
P a g e 52 Vol.10 Issue 5(Ver 1.0)September 2010 Subclass Of K Uniformly Starlike Functions Associated With Wright Generalized Hypergeometric Functions G.Murugusundaramoorthy 1, T.Rosy 2 And K.Muthunagai
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 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 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 informationInvariant Approximation Results of Generalized Contractive Mappings
Filomat 30:14 (016), 3875 3883 DOI 10.98/FIL1614875C Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Invariant Approximation Results
More information