Initial Coefficients and Fekete-Szegő Inequalities for Functions Related to van der Pol Numbers (VPN)

Author:

Murugusundaramoorthy Gangadharan1,Bulboacă Teodor2

Affiliation:

1. * Department of Mathematics, School of Advanced Science, Vellore Institute of Technology , Vellore - , TN . INDIA , gmsmoorthy@yahoo.com

2. ** Faculty of Mathematics and Computer Science, Babeş-Bolyai University , Cluj-Napoca , ROMANIA

Abstract

ABSTRACT The purpose of this paper is to find coefficient estimates for the class of functions N ( γ , ϑ , λ ) consisting of analytic functions f normalized by f(0) = f′(0) – 1 = 0 in the open unit disk D subordinated to a function generated using the van der Pol numbers, and to derive certain coefficient estimates for a 2, a 3, and the Fekete-Szegő functional upper bound for f N ( γ , ϑ , λ ) . Similar results were obtained for the logarithmic coefficients of these functions. Further application of our results to certain functions defined by convolution products with a normalized analytic functions is given, and in particular, we obtain Fekete-Szegő inequalities for certain subclasses of functions defined through the Poisson distribution series.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

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