The so-called R-function combines the generalized Gaussian hypergeometric function and generalized Mittag-Leffler function. The R-function is a generalization of well-known M-series which is defined to accommodate the well-known Srivastava-Tomovski operator. Using the Hadamard product, here we define a differential operator involving R-function which would include the convex combination of analytic function. Using the defined operator, here we define a new subclasses of starlike functions subordinate to the general function. The primary aim is to generalize and unify the study of various subclasses of univalent function theory. We derive the initial coefficient estimates and Fekete-Szego inequality for the defined function class. In the last section, we present applications involving results associated with vertical domain and Janowski function. Further by appropriate choice of parameters, we provided some new and well known results of our main result.
Umadevi et al. (Mon,) studied this question.