A Class of Analytic Functions with respect to Symmetric Points Involving Multiplicative Derivative

Abstract

Here we explore the behaviour and deviations of the geometric properties of a class of univalent functions when the classical derivative is replaced with a multiplicative derivative. The primary question that we will be addressing here is that given a more versatile calculus of Newton and Euler, why we need a study involving such a restrictive calculus so called as multiplicative calculus. Precisely, we introduce and study a new subclass of analytic function with respect to symmetric points using multiplicative derivative. We obtain the estimates for the initial coefficients and Fekete-Szegő inequalities of the same. We have included some examples to establish the inclusion and closure properties of our defined class. Further, we obtain the logarithmic and inverse coefficients for the defined function class.