On Janowski functions associated with (n,m)-symmetrical functions

Abstract

The aim in the present work is to introduce and study new subclasses of analytic functions that are defined by using the generalized classes of Janowski functions combined with the (n, m)-symmetrical functions, that generalize many others defined by different authors. We gave a representation theorem for these classes, certain inherently properties, while covering and distortion properties are also pointed out.

Coefficient Inequalities of a Comprehensive Subclass of Analytic Functions With Respect to Symmetric Points

“…Further, the classes recently introduced and studied by Sarari et al (2019) in [6] is closely related to the classes C (j,k) (b, c; λ, δ; ψ; G, H) and K (j,k) (b, c; λ, δ; ψ; G, H) defined by us here.…”

Geometric Properties of Certain Classes of Analytic Functions with Respect to (x,y)-Symmetric Points

“…Here, λ represents a real number such that its absolute value is less than π 2 . In recent research conducted by Al sarari et al [17,18], numerous intriguing findings were obtained for various classes by utilizing the concept of (x, y)-symmetrical functions and the q-derivative. Consequently, we combine the notion of (x, y)-symmetrical functions, the q-derivative, and Janowski-type functions to establish the ensuing classes.…”

Convolution Properties of q-Janowski-Type Functions Associated with (x,y)-Symmetrical Functions

“…Recently the authors of [3,4] obtained many interesting results for various classes using the concept of (x, y)-symmetrical functions and q-derivative.…”