Applications of Some Subclasses of Meromorphic Functions Associated with the <i>q</i>-Derivatives of the <i>q</i>-Binomials

Abstract

In this article, we make use of the q-binomial theorem to introduce and study two new subclasses ℵ(αq,q) and ℵ(α,q) of meromorphic functions in the open unit disk U, that is, analytic functions in the punctured unit disk U∗=U\{0}={z:z∈Cand0z1}. We derive inclusion relations and investigate an integral operator that preserves functions which belong to these function classes. In addition, we establish a strict inequality involving a certain linear convolution operator which we introduce in this article. Several special cases and corollaries of our main results are also considered.

Keywords

• q-derivatives of binomials
• Jackson’s q-integrals
• analytic functions
• starlike and convex functions
• analytic and meromorphic functions
• hadamard product (or convolution)