Applications of Ruscheweyh derivatives and Hadamard product to analytic functions

Abstract

For given analytic functions in U = {z | |z| < 1} with λm ≥ 0, μm ≥ 0 and λm ≥ μm, let En(ϕ, ψ; A, B) be the class of analytic functions in U such that (f*Ψ)(z) ≠ 0 and urn:x-wiley:01611712:media:ijmm978494:ijmm978494-math-0003 where is the nth Ruscheweyh derivative; ≪ and * denote subordination and the Hadamard product, respectively. Let T be the class of analytic functions in U of the form , and let En[ϕ, ψ; A, B] = En(ϕ, ψ; A, B)∩T. Coefficient estimates, extreme points, distortion theorems and radius of starlikeness and convexity are determined for functions in the class En[ϕ, ψ; A, B]. We also consider the quasi‐Hadamard product of functions in En[z/(1 − z), z/(1 − z); A, B] and En[z/(1−z)2, z/(1−z)2; A, B].