INITIAL COEFFICIENT ESTIMATES FOR SOME SUBCLASSES OF M-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS

doi:10.1016/S0252-9602(16)30045-5

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (3): 863-871.doi: 10.1016/S0252-9602(16)30045-5

INITIAL COEFFICIENT ESTIMATES FOR SOME SUBCLASSES OF M-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS

H. M. SRIVASTAVA^1,2, S. GABOURY³, F. GHANIM⁴

1. Department of Mathematics and Statistics, University of Victoria Victoria, British Columbia V8 W 3 R4, Canada;
2. China Medical University, Taichung 40402, Taiwan, China;
3. Department of Mathematics and Computer Science, University of Québec at Chicoutimi, Chicoutimi, Québec G7 H2 B1, Canada;
4. Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates

收稿日期:2015-03-02 修回日期:2015-05-26 出版日期:2016-06-25 发布日期:2016-06-25
通讯作者: S. GABOURY,E-mail:s1gabour@uqac.ca E-mail:s1gabour@uqac.ca
作者简介:H. M. SRIVASTAVA,E-mail:harimsri@math.uvic.ca;F. GHANIM,E-mail:fgahmed@sharjah.ac.ae

INITIAL COEFFICIENT ESTIMATES FOR SOME SUBCLASSES OF M-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS

H. M. SRIVASTAVA^1,2, S. GABOURY³, F. GHANIM⁴

1. Department of Mathematics and Statistics, University of Victoria Victoria, British Columbia V8 W 3 R4, Canada;
2. China Medical University, Taichung 40402, Taiwan, China;
3. Department of Mathematics and Computer Science, University of Québec at Chicoutimi, Chicoutimi, Québec G7 H2 B1, Canada;
4. Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates

Received:2015-03-02 Revised:2015-05-26 Online:2016-06-25 Published:2016-06-25
Contact: S. GABOURY,E-mail:s1gabour@uqac.ca E-mail:s1gabour@uqac.ca

摘要/Abstract

摘要：

In the present investigation, we consider two new general subclasses β_∑m(τ, λ; α) and β_∑m^*(τ, λ; β) of ∑_m consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk U. For functions belonging to the two classes introduced here, we derive non-sharp estimates on the initial coefficients|a_m+1|and|a_2m+1|. Several connections to some of the earlier known results are also pointed out.

关键词: analytic functions, bi-univalent functions, m-Fold symmetric functions, m-Fold symmetric bi-univalent functions

Abstract:

Key words: analytic functions, bi-univalent functions, m-Fold symmetric functions, m-Fold symmetric bi-univalent functions

中图分类号:

30C45

H. M. SRIVASTAVA, S. GABOURY, F. GHANIM. INITIAL COEFFICIENT ESTIMATES FOR SOME SUBCLASSES OF M-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS[J]. 数学物理学报(英文版), 2016, 36(3): 863-871.

H. M. SRIVASTAVA, S. GABOURY, F. GHANIM. INITIAL COEFFICIENT ESTIMATES FOR SOME SUBCLASSES OF M-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS[J]. Acta mathematica scientia,Series B, 2016, 36(3): 863-871.

参考文献

[1] Brannan D A, Clunie J G, eds. Aspects of Contemporary Complex Analysis (Proceedings of the NATO Advanced Study Institute held at the University of Durham, Durham; July 1-20,1979). New York, London: Academic Press, 1980
[2] Brannan D A, Taha T S. On some classes of bi-univalent functions. Studia Univ Babe?-Bolyai Math, 1986, 31(2): 70-77
[3] Duren P L. Univalent Functions. Grundlehren der Mathematischen Wissenschaften, 259. Berlin: Springer-Verlag, 1983
[4] Frasin B A, Aouf M K. New subclasses of bi-univalent functions. Appl Math Lett, 2011, 24: 1569-1573
[5] Hayami T, Owa S. Coefficient bounds for bi-univalent functions. Pan Amer Math J, 2012, 22(4): 15-26
[6] Koepf W. Coefficients of symmetric functions of bounded boundary rotations. Proc Amer Math Soc, 1989, 105: 324-329
[7] Lewin M. On a coefficient problem for bi-univalent functions. Proc Amer Math Soc, 1967, 18: 63-68
[8] Li X-F, Wang A-P. Two new subclasses of bi-univalent functions. Int Math Forum, 2012, 7: 1495-1504
[9] Löwner K. Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. Math Ann, 1923, 89: 103-121
[10] Pommerenke C. On the coefficients of close-to-convex functions. Michigan Math J, 1962, 9: 259-269
[11] Pommerenke C. Univalent Functions (with a Chapter on Quadratic Differentials by Gerd Jensen). Göttingen: Vandenhoeck and Ruprecht, 1975
[12] Srivastava H M, Gaboury S, Ghanim F. Coefficient estimates for some general subclasses of analytic and bi-univalent functions. Preprint, 2015: 1-13
[13] Srivastava H M, Gaboury S, Ghanim F. Coefficient estimates for an unification of some subclasses of analytic and bi-univalent functions of Ma-Minda type. Preprint, 2015: 1-9
[14] Srivastava H M, Magesh N, Yamini J. Initial coefficient estimates for bi-lambda-convex and bi-mu-starlike functions connected with arithmetic and geometric means. Electron J Math Anal Appl, 2014, 2: 152-162(electronic)
[15] Srivastava H M, Mishra A K, Gochhayat P. Certain subclasses of analytic and bi-univalent functions. Appl Math Lett, 2010, 23: 1188-1192
[16] Srivastava H M, Owa S, eds. Current Topics in Analytic Function Theory. Singapore: World Scientific, 1992
[17] Srivastava H M, Sivasubramanian S, Sivakumar R. Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions. Tbilisi Math J, 2014, 7(2): 1-10
[18] Styer D, Wright J. Result on bi-univalent functions. Proc Amer Math Soc, 82(1981), 243-248
[19] Tan D-L. Coefficicent estimates for bi-univalent functions. Chinese Ann Math Ser A, 1984, 5: 559-568
[20] Xu Q-H, Gui Y-C, Srivastava H M. Coefficient estimates for a certain subclass of analytic and bi-univalent functions. Appl Math Lett, 2012, 25: 990-994
[21] Xu Q-H, Xiao H-G, Srivastava H M. A certain general subclass of analytic and bi-univalent functions and associated coefficient estimates problems. Appl Math Comput, 2012, 218: 11461-11465

INITIAL COEFFICIENT ESTIMATES FOR SOME SUBCLASSES OF M-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS

INITIAL COEFFICIENT ESTIMATES FOR SOME SUBCLASSES OF M-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS

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