New Subclasses Of Bi-Univalent Functions Defined By (p, q)-Derivative Operator Subordinate To Lucas-Balancing Polynomials

Author : Luminita-Ioana Cotirla

Abstract :Our current study is primarily driven by the abundance of fascinating and productive applications for a broad class of special polynomials. One such special polynomial is the Lucas-balancing polynomials, which have recently been examined in geometric function theory. This paper’s main goal is to introduce and study two subclasses of analytic and bi-univalent functions defined by the (p, q)-derivative operator subordinate to Lucas-Balancing polynomials. We obtain the estimates for function coefficients |d2| and |d3| of the newly created classes. We also estimate the Fekete-Szeg¨o problem |d2 −µd2 3 |, µ ∈ R for functions in these classes. We also present a number of findings from our research and draw attention to relevant connections with earlier findings. 2020 MSC: 30C45, 33C45; 11B39.

Keywords :Bi-univalent, (p, q)-derivative operator, Subordination, Lucas-Balancing polynomials, Fekete-Szeg¨o functional.

Conference Name :International Conference on Mathematical Sciences & Computer Engineering (ICMSCE-25)

Conference Place Zurich, Switzerland

Conference Date 11th Apr 2025