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Further Development of the Fekete-Szegö│a3 - μa22│-Functional Inequality for Classes of Analytic Functions Based on Differential Operators and Subclasses

DOI: 10.4236/oalib.1112052, PP. 1-12

Subject Areas: Mathematics

Keywords: Analytic Functions, Fekete-Szegö, Problem, Subclass, Hadamard Product, Linear Operator, Strongly Starlike Functions, Strongly Convex Functions

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Abstract

In mathematics, the Fekete-Szegö inequality is an inequality for the coefficients of univalent analytic functions found by Fekete and Szegö (1933), related to the Bieberbach conjecture. Finding similar estimates for other classes of functions is called the Fekete-Szeg? problem. In this paper, I study to solve the Fekete-Szegö problem for │a3 - μa22│ -functional inequalities with μ is real or complex by the generalized linear differential operator. That is the main result in this paper.

Cite this paper

An, L. V. (2024). Further Development of the Fekete-Szegö│a3 - μa22│-Functional Inequality for Classes of Analytic Functions Based on Differential Operators and Subclasses. Open Access Library Journal, 11, e2052. doi: http://dx.doi.org/10.4236/oalib.1112052.

References

[1]  Fekete, M. and Szegö, G. (1933) Eine Bemerkung über Ungerade Schlichte Funktionen. Journal of the London Mathematical Society, 1, 85-89. https://doi.org/10.1112/jlms/s1-8.2.85
[2]  Pfluger, A. (1986) The Fekete—Szegö Inequality for Com-plex Parameters. Complex Variables, Theory and Application: An International Journal, 7, 149-160. https://doi.org/10.1080/17476938608814195
[3]  Keogh, F.R. and Merkes, E.P. (1969) A Coefficient Inequality for Certain Classes of Analytic Functions. Proceedings of the American Mathematical Society, 20, 8-12. https://doi.org/10.1090/s0002-9939-1969-0232926-9
[4]  Ma, W. and Minda, D. (1991) An Internal Geometric Char-acterization of Strongly Starlike Functions. Annales Universitatis Mariae Curie-Sklodowska, Sectio A, 45, 89-97.
[5]  Ma, W. and Minda, D. (1997) Coefficient Inequalities for Strongly Close-To-Convex Functions. Journal of Mathematical Analysis and Applications, 205, 537-553. https://doi.org/10.1006/jmaa.1997.5234
[6]  Carlson, B.C. and Shaffer, D.B. (1984) Star-like and Prestarlike Hypergeometric Functions. SIAM Journal on Mathematical Analysis, 15, 737-745. https://doi.org/10.1137/0515057
[7]  Ruscheweyh, S. (1975) New Criteria for Univalent Functions. Proceedings of the American Mathematical Society, 49, 109-115. https://doi.org/10.1090/s0002-9939-1975-0367176-1
[8]  Dziok, J. (1999) Classes of Functions Defined by Certain Differential-Integral Operators. Journal of Computational and Applied Mathematics, 105, 245-255. https://doi.org/10.1016/s0377-0427(99)00014-x
[9]  Lashin, A.Y. (2003) Starlike and Convex Functions of Complex Order Involving a Certain Linear Operator. Indian Journal of Pure and Applied Mathematics, 34, 1101-1108.
[10]  Ravichandran, V. and Kumar, S.S. (2004) On a Class of Analytic Functions Involving Carlson-Shaffer Linear Operator. Rivista di Matematica della Università di Parma, 7, 35-48.
[11]  Srivastava, H.M. and Owa, S. (1992) Cur-rent Topics in Analytic Function Theory. World Scientific Publishing. https://doi.org/10.1142/1628
[12]  Raducanu, D. and Orhan, H. (2010) Subclasses of Analytic Functions Defined by a Generalized Differential Operator. International Journal of Mathematical Analysis, 4, 1-15.
[13]  Abdel-Gawad, H.R. and Thomas, D.K. (1992) The Fekete-Szegö Problem for Strongly Close-To-Convex Functions. Proceedings of the American Mathematical Society, 114, 345-349. https://doi.org/10.1090/s0002-9939-1992-1065939-0
[14]  Çağlar, M., Deniz, E. and Orhan, H. (2011) Coefficient Bounds for a Subclass of Starlike Functions of Complex Order. Applied Mathematics and Computation, 218, 693-698. https://doi.org/10.1016/j.amc.2011.01.085
[15]  Darus, M. and Akbarally, A. (2004) Coefficient Estimates for Ruschew-eyh Derivatives. International Journal of Mathematics and Mathematical Sciences, 2004, 1937-1942. https://doi.org/10.1155/s0161171204309051
[16]  Deniz, E. and Orhan, H. (2010) The Fekete-Szegö Problem for a Generalized Subclass of Analytic Functions. Kyungpook Mathematical Journal, 50, 37-47. https://doi.org/10.5666/kmj.2010.50.1.037
[17]  Deniz, E., Çağlar, M. and Orhan, H. (2012) The Fekete-Szegö Problem for a Class of Analytic Functions Defined by Dziok-Srivastava Operator. Kodai Mathematical Journal, 35, 439-462. https://doi.org/10.2996/kmj/1352985448
[18]  Frasin, B. and Darus, M. (2003) On Fekete-Szego Problem Using Hada-mard Product. The International Journal of Mathematics and Mathematical Sciences, 12, 1289-1295.
[19]  Goel, R.M. and Mehrok, B.S. (1991) A Coefficient Inequality for Certain Classes of Analytic Functions. Tamkang Journal of Mathematics, 22, 153-163. https://doi.org/10.5556/j.tkjm.22.1991.4588
[20]  Keogh, F.R. and Merkes, E.P. (1969) A Coefficient Inequality for Certain Classes of Analytic Functions. Proceedings of the American Mathematical Society, 20, 8-12. https://doi.org/10.1090/s0002-9939-1969-0232926-9
[21]  Orhan, H. and Kamali, M. (2003) On the Fekete-Szegö Problem. Applied Mathematics and Computation, 144, 181-186. https://doi.org/10.1016/s0096-3003(02)00426-5
[22]  Orhan, H. and Răducanu, D. (2009) Fekete-Szegö Problem for Strongly Starlike Functions Associated with Generalized Hypergeometric Functions. Mathematical and Computer Modelling, 50, 430-438. https://doi.org/10.1016/j.mcm.2009.04.014
[23]  Orhan, H., Yagmur, N. and Deniz, E. (2011) Coefficient Inequality for a Generalized Subclass of Analytic Functions. Bulletin of the Transilvania University of Brasov. Series III, 4, 51-57.
[24]  Orhan, H., Deniz, E. and Çağlar, M. (2012) Fekete-Szegö Problem for Certain Subclasses of Analytic Functions. Demonstratio Mathematica, 45, 835-846. https://doi.org/10.1515/dema-2013-0423
[25]  Srivastava, H.M., Mishra, A.K. and Das, M.K. (2001) The Fekete-Szegö-Problem for a Subclass of Close-to-Convex Functions. Complex Variables, Theory and Application: An International Journal, 44, 145-163. https://doi.org/10.1080/17476930108815351
[26]  Văn An, L. (2023) The Fekete-Szego Problem of Analytic Functions Based on the Deferential Opertor and Certain Subclasses. Journal of Advances in Mathematics, 22, 40-52. https://doi.org/10.24297/jam.v22i.9499

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