On the Fekete–Szegö Problem for Meromorphic Functions Associated with <i>p</i>,<i>q</i>-Wright Type Hypergeometric Function

Abstract

Making use of a post-quantum derivative operator, we define two classes of meromorphic analytic functions. For the considered family of functions, we aim to investigate the sharp bounds’ values in the case of the Fekete–Szegö problem. The study of the well-known Fekete–Szegö functional in the post-quantum calculus case for meromorphic functions provides new outcomes for research in the field. With the extended p,q-operator, we establish certain inequalities’ relations concerning meromorphic functions. In the final part of the paper, a new p,q-analogue of the q-Wright type hypergeometric function is introduced. This function generalizes the classical and symmetrical Gauss hypergeometric function. All the obtained results are sharp.

Keywords

• meromorphic functions
• Fekete–Szegö problem
• <i>p</i>,<i>q</i>-derivative operator
• <i>p</i>,<i>q</i>-Wright type hypergeometric function