Application of Integral Operator Generated by Touchard Polynomials to Certain Subclasses of Harmonic Functions

Abstract

Let SH denote the class of functions f = h + g which are harmonic univalent and sense-preserving in the unite disk U = {z : |z| < 1} where h(z) = z +P∞ k=2 akzk, g(z) =∞Pk=1 bkzk (|b1| < 1). In this paper we establish connections between various subclasses of harmonic univalent functions by applying certain integral operator involving the Touchard Polynomials.