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Application of Gegenbauer polynomials to certain classes of bi-univalent functions of order $\nu+i\varsigma$

MASLINA DARUS|Omar Alnajar|Ala Amourah
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2024.03|한국수학논문집 (Korean Journal of Mathematics)|제32권 제1호|pp. 183-193

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키워드

bi-univalent functionsGegenbauer polynomialsHolomorphic functionsFekete and Szeg"{o} problem
주제분류수학

초록

In this paper, a new class of bi-univalent functions that are described by Gegenbauer polynomials is presented. We obtain the estimates of the Taylor-Maclaurin coefficients $ \left\vert m_{2}\right\vert $ and $\left\vert m_{3}\right\vert $ for each function in this class of bi-univalent functions. In addition, the Fekete--Szeg\"{o} problems function new are also studied.

Abstract

In this paper, a new class of bi-univalent functions that are described by Gegenbauer polynomials is presented. We obtain the estimates of the Taylor-Maclaurin coefficients $ \left\vert m_{2}\right\vert $ and $\left\vert m_{3}\right\vert $ for each function in this class of bi-univalent functions. In addition, the Fekete--Szeg\"{o} problems function new are also studied.

참고문헌 (28)

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관련 논문AI추천

Coefficient Estimates for a Subclass of Bi-univalent Functions Associated with Symmetric q-derivative Operator by Means of the Gegenbauer PolynomialsAla Amourah, Basem Aref Frasin, Tariq Al-Hawary경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2022 · 제62권 제2호Gegenbauer Polynomials For a New Subclass of Bi-univalent FunctionsAbbas Kareem Wanas, Balasubramaniam Vanithakumari, Gunasekar Saravanan, Sudharsanan Baskaran경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2024 · 제64권 제3호COEFFICIENT BOUNDS FOR CERTAIN SUBCLASSES OF BI-PRESTARLIKE FUNCTIONS ASSOCIATED WITH THE GEGENBAUER POLYNOMIALG. MURUGUSUNDARAMOORTHY, H. Ö. guney, K. Vijaya장전수학회 · Advanced Studies in Contemporary Mathematics2022 · 제32권 제1호INITIAL COEFFICIENT BOUNDS FOR SUBCLASSES OF BI-UNIVALENT FUNCTIONS ASSOCIATED WITH THE CHEBYSHEV POLYNOMIALSG. MURUGUSUNDARAMOORTHY, HATUN OZLEM GUNEY, K. VIJAYA장전수학회 · Advanced Studies in Contemporary Mathematics2018 · 제28권 제3호Coefficient estimates for a subclass of analytic bi-univalent functionsAhmad Zireh, Ebrahim Analouei Adegani, Serap Bulut대한수학회 · 대한수학회보2018 · 제55권 제2호Sharp bounds for the initial coefficients for certain families of bi-univalent functionsAhmad Motamednezhad, Safa Salehian대한수학회 · 대한수학회논문집2024 · 제39권 제4호

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