Some New Results of Differential Subordinations for HigherOrder Derivatives of Multivalent Functions

Abstract

The main purpose of this paper is to study the differential subordination result for multivalent analytic functions. We give some applications of higher-order differential subordination results involving Hadamard product for multivalent analytic functions with generalized hypergeometric function in open unit disk. We have also discussed and studied a new class of higher-order derivatives of multivalent analytic functions in open unit disk of complex plane related to linear operator and we obtain some results connected inclusion relationship, argument estimate, integral representation and subordination property. by using the method of differential subordination we aim to prove some classical results in multivalent functions theory. We obtain some interesting properties of this class and establish several strong differential subordination for higher-order derivatives of multivalent analytic functions. By making use of the principle of subordination, we introduce a new class W_(p, q)^(l, k) (η,α_1, m; h) for higher-order derivatives of multivalent analytic functions associated with Dziok-Srivastava operator. We obtain some result for this class.

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

“…A univalent function q is named a dominant of the solutions of the differential subordination if 𝒷 ≺ 𝑞 for all 𝑝 satisfying (4). A dominant 𝑞 ̃(𝜈) that satisfies 𝑞 ̃≺ 𝑞 for all dominants q of ( 4 Many scholars have discussed and dealt with second-order differential subordina tion and superordination, see [11,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]). Several authors have recently written abou superordination and the principle of third-order differential subordination.…”

“…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.…”

On Some Sandwich Results of Univalent Functions Related by Differential Operator

“…Using the results (see [11,[18][19][20][21][22][23][24][25][26][27][28][29][30][31]) t𝑜 o𝑏𝑡ain suffici𝑒nt co𝑛𝑑itions for normalized an𝑎lytic functi𝑜ns to s𝑎𝑡isfy:…”

“…Als𝑜, Al-Ameedee et al [18,19] and El-Ashwah and Aouf [3] derived s𝑜me diff𝑒𝑟𝑒ntial sub𝑜𝑟𝑑ination an𝑑 sup𝑒𝑟𝑜rdination r𝑒𝑠ults f𝑜r analytic f𝑢nctions in 𝕌. Recently, several researchers obtained sandwich theorems for subclasses of analytic functions (see [3,[5][6][7][8]10,[12][13][14]18,20,[26][27][28][29][30][31]) .…”

Revised Manuscript On New Sandwich Results of Univalent Functions Defined by a Linear Operator

“…Recently, several authors [2,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] gave sandwich-type sequences for types of analytic functions using another sufficient conditions . 2.…”