Comprehensive family of $k$-uniformly harmonic starlike functions

Abstract

In this paper, we introduce a comprehensive family of k-uniformly harmonicunivalent functions which contains various well-known classes of harmonicunivalent functions as well as many new ones. Coefficient bounds, distortionbounds, extreme points, convolution conditions, and convex combination aredetermined for functions in this family. Further results on integraltransforms are discussed. Consequently, many of our results are eitherextensions or new approaches to those corresponding previously known results.