On New Symmetric Schur Functions Associated with Integral and Integro-Differential Functional Expressions in a Complex Domain

Abstract

The symmetric Schur process has many different types of formals, such as the functional differential, functional integral, and special functional processes based on special functions. In this effort, the normalized symmetric Schur process (NSSP) is defined and then used to determine the geometric and symmetric interpretations of mathematical expressions in a complex symmetric domain (the open unit disk). To obtain more symmetric properties involving NSSP, we consider a symmetric differential operator. The outcome is a symmetric convoluted operator. Geometrically, studies are presented for the suggested operator. Our method is based on the theory of differential subordination.

Univalence and Starlikeness of Certain Classes of Analytic Functions

“…Currently, as an application of the Ozaki inequality, many classes of analytic functions involve polynomials, special functions and different types of operators of the normalized class are investigated. For example, the starlikeness property is studied in [8][9][10]; the convex property is checked in [11][12][13] and the close to convex property is realized in [14,15]. In this effort, we proceed with the investigation on univalency and starlikeness of the normalized class.…”