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

ABSTRACT The purpose of this paper is to find coefficient estimates for the class of functions ℳ 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 ∈ ℳ 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.