AN APPLICATION OF FRACTIONAL CALCULUS TO HARMONIC UNIVALENT FUNCTIONS

摘要

In this paper authors introduce a new subclass S_(H,λ)~*(α) of S_H by using fractional calculus. We give univalence criteria and sufficient coefficient conditions for normalized harmonic functions belonging to the class S_(H,λ)~*(α), where (0 ≤ α < 1), (0 ≤ λ < 1). These coefficient conditions are also shown to be necessary for subclass TS_(H,λ)~*(α) of S_(H,λ)~*(α) in which h has negative and g has positive coefficients. This leads to extreme points, distortion bounds and radius of convexity. We also discuss a class preserving integral operator and show that the class studied in this paper is closed under convolution and convex combinations.