New and Extended Results On Fourth-Order Differential Subordination for Univalent Analytic Functions

Abstract

In this paper, we introduce new concept that is fourth-order differential subordination and superordination associated with linear operator for univalent analytic functions in open unit disk. Here, we extended some lemmas. Also some interesting new results are obtained.

Coefficient estimates for certain subclasses of analytic functions defined by new operator

“…In references ( [12][13][14][15][16][17][18][19][20]) can be found similar studies on analytical functions in recent years.…”

New Results on Higher-Order Differential Subordination and Superordination for Univalent Analytic Functions Using a New Operator

“…satisfy the fourth-order differential subordination condition, ψ( subordination by Atshan et al [9,10,[12][13][14]. The third-order case was extended to fourth-order differential subordination and discovered characteristics of functions meeting the fourth-order differential subordination: 𝜙(𝑓(𝜈), 𝜈𝑓 ′ (𝜈), 𝜈 2 𝑓 ′′ (𝜈), 𝜈 3 𝑓 ′′′ (𝜈), 𝜈 4 𝑓 ′′′′ (𝜈); 𝜈) ≺ ℎ(𝜈),…”

“…(ν), ν 2 subordination by Atshan et al [9,10,[12][13][14]. The third-order case was extend fourth-order differential subordination and discovered characteristics of func meeting the fourth-order differential subordination:…”

“…Third-order differential inequalities in the complex plane were considered in 1992 [3], and the concept of third-order differential subordination was introduced in 2011 by Antonino and Miller [4]. Further investigations were conducted on third-order differential subordination results for univalent analytic functions involving an operator [5][6][7][8] and, continuing the idea, the concept of fourth-order differential subordination was introduced and studied in 2020 [9,10]. Further results were published in 2021 and 2022 [11][12][13][14] regarding the new concepts of higher-order differential subordinations.…”

“…Further investigations were conducted on third-order differential subordination results for univalent analytic functions involving an operator [5][6][7][8] and, continuing the idea, the concept of fourth-order differential subordination was introduced and studied in 2020 [9,10]. Further results were published in 2021 and 2022 [11][12][13][14] regarding the new concepts of higher-order differential subordinations. The present paper continues this study.…”