Properties of a Class of Analytic Functions Influenced by Multiplicative Calculus

Abstract

Motivated by the notion of multiplicative calculus, more precisely multiplicative derivatives, we used the concept of subordination to create a new class of starlike functions. Because we attempted to operate within the existing framework of the design of analytic functions, a number of restrictions, which are in fact strong constraints, have been placed. We redefined our new class of functions using the three-parameter Mittag–Leffler function (Srivastava–Tomovski generalization of the Mittag–Leffler function), in order to increase the study’s adaptability. Coefficient estimates and their Fekete-Szegő inequalities are our main results. We have included a couple of examples to show the closure and inclusion properties of our defined class. Further, interesting bounds of logarithmic coefficients and their corresponding Fekete–Szegő functionals have also been obtained.

An Efficient Solution of Multiplicative Differential Equations through Laguerre Polynomials

“…This has paved the way for the utilization of multiplicative calculus in various aspects of practical life. Example application areas are biomedical image analysis [5], economics [6], time-scale theory [7], chemical engineering [8], processing of real-world signals [9], fractional dynamical systems [10], and digital image interpolation [11]. A recent study developed an analytical model to predict COVID-19 spread by incorporating multiplicative calculus into machine learning [12].…”