Generalization of Quasi Convex Functions using Convolution

Abstract

In this paper, an up-to-date generalization of the class $\mathtt{C^\star}$ of quasi-convex functions is given by introducing new class $\mathfrak{\mathtt{C}^\star_g[a, b]}$. Furthermore its basic properties, its relationship with other subclasses of $\mathtt{S}$, inclusion relations and some other interesting properties are derived.