PROPERTIES OF CERTAIN CLASSES OF ANALYTIC FUNCTIONS DEFINED BY SRIVASTAVA-ATTIYA OPERATOR

摘要

In this paper we introduce the class K(s,b,β, a) of analytic functions defined by the Srivastava—Attiya convolution operator Js,b(f) involving the Hurwitz—Lerch Zeta function. We derive few subordination results for the functions in the class K(s, b, β, a) and discuss the interesting applications of subordination results with the help of convex functions. Several other properties like coefficient inequalities growth and distortion theorems, extreme points, integral mean inequalities, partial sums and quasiHadamard product are investigated for the class K ( s,b, β, a). The authors also obtain Fekete-Szegso inequality for normalized analytic functions f (z) defined on the open unit disc for which z(.1s,b f )' (z) + (1 — 13)(J.,,b f)(z) (0 < [3 < 1) z(Js,bf)'(z) z2 (Js,b f)" (z) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Ap- Olications of our main result involving the Owa-Srivastava operator of fractional calculus ire discussed. Finally as one of the applications of our result, we derive the Fekete—Szego inequality for a class of normalized analytic functions, defined using the Hadamard product and the Owa-Srivastava operator.