On classes of non-univalent functions influenced by the multiplicative derivative

In this article, we extend studies on the class of starlike functions, motivated by the definition of the multiplicative derivative. In this direction, we define a new class by combining characterizations of starlike functions and a recently studied subclass of analytic functions. Furthermore, we have defined a new family of analytic functions motivated by the so-called theta-starlike function. Here, we discussed in detail the problems and repercussions of employing a non-Newtonian derivative in studies of various subclasses of analytic functions. Fekete-Szegő inequality and bounds of initial coefficients are our main results. Although our main results have numerous applications, here we highlight the results associated with the conic regions as applications of the main results.