A Study of Multivalent <i>q</i>-starlike Functions Connected with Circular Domain

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.

Keywords

• multivalent functions
• <i>q</i>-Ruschweyh differential operator
• <i>q</i>-starlike functions
• circular domain
• <i>q</i>-Bernardi integral operator