A GENERALIZED CLASS OF HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH AL-OBOUDI OPERATOR INVOLVING CONVOLUTION

Abstract

In this paper, we have introduced a generalized class S_H^i (m, n, γ, φ, ψ; α), i ∈ {0, 1} of harmonic univalent functions in unit disc U, a sufficient coefficient condition for the normalized harmonic function in this class is obtained. It is also shown that this coefficient condition is necessary for its subclass T S_H^i (m, n, γ, φ, ψ; α). We further obtained extreme points, bounds and a covering result for the class T S_H^i (m, n, γ, φ, ψ; α). Also, show that this class is closed under convolution and convex combination. While proving our results, certain conditions related to the coefficients of φ and ψ are considered, which lead to various well-known results.