Marx-Strohhacker inequality for Mocanu-Janowski alpha-convex functions

Abstract

Let be the class of functions w(z) regular in the unit disc D = {z : |z| < 1} with w(0) = 0, and |w(z)| < 1. For arbitrarily fixed real numbers A 2 ( 1,1) and B 2 ( 1,A), let P(A, B) be the class of regular functions p(z) in D such that p(0) = 1, and p(z) 2 P(A, B) if and only if p(z) = 1+Aw(z) 1+Bw(z) for every z 2 D, for some w(z) 2 . In the present paper we apply the subordination principle to give new proofs