Subordination Properties of Multivalent Functions Defined by Generalized Multiplier Transformation

Abstract

The main object of the present paper is to investigate several interesting subordination properties and a sharp inclusion relationship for certain subclass of multivalent analytic functions, which are defined here by the generalized multiplier transformation. Relevant connections of the results which are presented in this paper with various known results are also considered.

Fekete-Szegӧ Functional for Classes X_q^n (φ) and Y_q^n (φ)

“…The definition of subordination according to Jeyaraman & Suresh [6] is as if 𝑓 and 𝑔 are in 𝐴, the function 𝑓 is said to be subordinate to 𝑔 or (equivalently) 𝑔 is said to be superordinate to 𝑓, 𝑓 ≺ 𝑔 in 𝕌 or 𝑓(𝑧) ≺ 𝑔(𝑧) (𝑧 ∈ 𝕌)…”

The Subclasses of Analytic Functions of Complex Order with Application of q-Derivative Operators

“…By Jeyaraman and Suresh (2014) , if f and g are represented by the analytic functions in 𝕆, then the subordinate to g is f denoted as f ≺ g in 𝕆 or f (𝜁 ) ≺ g (𝜁 ) for all 𝜁 ∈ 𝕆 if the presence of the Schwarz function w(𝜁 ) is analytic in 𝕆 that has the properties |w(𝜁 )| < 1 and w(0) = 0 for all 𝜁 ∈ 𝕆 such that…”