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The purpose of this paper is to find coefficient estimates for the class of functionsℳ  N    (   γ  ,  ϑ  ,  λ   )consisting of analytic functions  f  normalized by  f (0) =  f′ (0) – 1 = 0 in the open unit diskDsubordinated 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 forf  ∈   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.

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