New class of k-uniformly harmonic functions defined by Al-Oboudi operator

Abstract

In this paper, we introduce the class $k$-USH $(u,v,\alpha,\lambda)$ using Al-Oboudi operator which is a subclass of $k$-uniformly harmonic functions. A subclass $k$-UTH $(u,v,\alpha,\lambda)$ of $k$-USH $(u,v,\alpha,\lambda)$ is also been defined and studied in this paper. Extreme points, distortion bounds, convolution condition and convex combination of functions belonging to the class $k$-UTH $(u,v,\alpha, \lambda)$ are also studied.