Applications of a Hurwitz-Lerch Zeta Linear Operator Involving Classes of Meromorphic Functions

Abstract

The findings of this study are connected with geometric function theory and were acquired by using linear operator is applied to investigate specific classes of meromorphic functions defined using the subordination. The first class introduced and investigated here, , is a generalized class of meromorphic functions. It is also shown that for particular choice of parameters for the new generalized class, the class of close-to-convex meromorphic functions emerges. Using the properties of the convolution and subordination, certain characterization properties of this class are proved involving combinations of the functions from the class. Further, three more classes, , , and , are defined in connection to this first class, developing new applications of this operator. The connections between the classes are given in the definition or in associated remarks and characterization properties are also proved, including combinations of functions belonging to those classes and inclusion relations.