Starlike functions associated with Q-multiplicative derivative

The rate of change of a function in the sense of multiplicative complex derivative, expressed in terms of quantum derivative, has not been used to study the various subclasses of univalent functions. Here, we attempt to define a new family of analytic functions by replacing the ordinary derivative in the analytic characterization of the starlike function with a quantity influenced by the definition of Q-multiplicative derivative. We explore the properties of a class of functions involving such a restrictive calculus. We obtain the estimates for the initial coefficients and Fekete-Szeg˝o inequalities of the defined function classes. Also, we have obtained the coefficient estimates for the inverse function.