Abstract
Starlike functions have gained popularity both in literature and in usage over the past decade. In this paper, our aim is to examine some useful problems dealing with q-starlike functions. These include the convolution problem, sufficiency criteria, coefficient estimates, and Fekete–Szegö type inequalities for a new subfamily of analytic and multivalent functions associated with circular domain. In addition, we also define and study a Bernardi integral operator in its q-extension for multivalent functions. Furthermore, we will show that the class defined in this paper, along with the obtained results, generalizes many known works available in the literature.
Highlights
The study of q-extension of calculus and q-analysis has attracted and motivated many researchers because of its applications in different parts of mathematical sciences
As an interesting sequel to [3], in which the q-derivative operator was used for the first time for studying the geometry of q-starlike functions, a firm footing of the usage of the q-calculus in the context of Geometric Function Theory was provided and the basic hypergeometric functions were first used in Geometric Function Theory in a book chapter by Srivastava (see, for details, [4])
Motivated by these q-developments in Geometric Function Theory, many authors added their contributions in this direction which has made this research area much more attractive in works like [4,12]
Summary
Lei Shi 1 , Qaiser Khan 2 , Gautam Srivastava 3,4 , Jin-Lin Liu 5 and Muhammad Arif 2,∗. Research Center for Interneural Computing, China Medical University, Taichung 40402, Taiwan
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