Bi-univalent functions subordinated to a three leaf function induced by multiplicative calculus

Abstract

Our aim was to develop a new class of bi starlike functions by utilizing the concept of subordination, driven by the idea of multiplicative calculus, specifically multiplicative derivatives. Several restrictions were imposed, which were indeed strict constraints, because we have tried to work within the current framework or the design of analytic functions. To make the study more versatile, we redefined our new class of function with Miller-Ross Poisson distribution (MRPD), in order to increase the study's adaptability. We derived the first coefficient estimates and Fekete-Szegő inequalities for functions in this new class. To demonstrate the characteristics, we have provided a few examples.

Keywords

• analytic function
• bi-univalent function
• convolution
• miller-ross function
• multiplicative calculus
• subordination
• poisson distribution