Coefficient bounds for a class of symmetric-starlike function defined by the Salagean operator
Applicable Nonlinear Analysis, Volume 2, Issue 3, December 2025, Pages: 159–166
WURAOLA TINUADE ADEMOSU
Department of Mathematics, University of Ilorin, P.M.B. 1515, Ilorin, Nigeria and Department of Mathematics, Covenant University, Ota, Nigeria
OLUWASEYI DAVID OLAWUMI
Department of Mathematics, University of Ilorin, P.M.B. 1515, Ilorin, Nigeria and Department of Mathematics, Covenant University, Ota, Nigeria
MARYJOY OBIAGERI EZUGORIE
Department of Mathematics, University of Ilorin, P.M.B. 1515, Ilorin, Nigeria and Department of Mathematics, Covenant University, Ota, Nigeria
ISHIAKU ZUBAIRU
Department of Mathematics, University of Ilorin, P.M.B. 1515, Ilorin, Nigeria and Department of Mathematics, Covenant University, Ota, Nigeria
OLUBUNMI ABIDEMI FADIPE-JOSEPH
Department of Mathematics, University of Ilorin, P.M.B. 1515, Ilorin, Nigeria and Department of Mathematics, Covenant University, Ota, Nigeria
Abstract
Complex analysis provides the foundation for understanding analytic functions while Geometric Function Theory (GFT), a branch of complex analysis investigates the geometric aspects of analytic functions exploring their properties and behavior. In GFT, coefficient problems focus on finding bounds and relationship among the coefficients of analytic functions which plays an important role in studying their geometric properties. Symmetric starlike function is a class of analytic functions that exhibit a specific type of symmetry and is starlike with respect to a symmetric point. Researchers have explored various subclasses of symmetric starlike functions, including those related to q-calculus, Janowski type functions, and conic domains. Previous studies investigated coefficient inequalities, sufficient conditions, convolution properties, and other geometric characteristics for classes of symmetric starlike functions. Many operators are being used in the study of analytic functions. Salagean introduced differential and integral operators which are the most interesting of all. These operators are very inspiring and many researchers in GFT are establishing results using the operators. The focus of this study is on symmetric-starlike function which was defined using Salagean differential operator and subordinate to the Gegenbauer polynomial. The initial coefficient bounds, Fekete-Szego and second Hankel determinant were obtained. Furthermore, Zalcman functional and the Krushkal inequality for the class of the Salagean type symmetric-starlike function were established.
Cite this Article as
Wuraola Tinuade Ademosu, Oluwaseyi David Olawumi, Maryjoy Obiageri Ezugorie, Ishiaku Zubairu, and Olubunmi Abidemi Fadipe-Joseph, Coefficient bounds for a class of symmetric-starlike function defined by the Salagean operator, Applicable Nonlinear Analysis, 2(3), 159–166, 2025