New Subclass of Close-to-Convex Functions Defined by Quantum Difference Operator and Related to Generalized Janowski Function

Abstract

This work begins with a discussion of the quantum calculus operator theory and proceeds to develop and investigate a new family of close-to-convex functions in an open unit disk. Considering the quantum difference operator, we define and study a new subclass of close-to-convex functions connected with generalized Janowski functions. We prove the necessary and sufficient conditions for functions that belong to newly defined classes, including the inclusion relations and estimations of the coefficients. The Fekete–Szegő problem for a more general class is also discussed. The results of this investigation expand upon those of the previous study.

Keywords

• analytic functions
• q-derivative (q-difference) operator
• close-to-convex functions
• Schwarz lemma
• subordination
• Janowski functions