Results on Third-Order Differential Subordination for Analytic Functions Related to a New Integral Operator

Abstract

In this paper, we aim to give some results for third-order differential subordination for analytic functions in the open unit disk 𝒰 = {𝑧:𝑧 ∈ ℂ and |𝑧𝑧|< 1} involving the new integral operator 𝜇m𝛼,𝑛(𝑓 ∗ 𝑔). The results are obtained by examining pertinent classes of acceptable functions. New findings on differential subordination have been obtained. Additionally, some specific cases are documented. This work investigates appropriate classes of admissible functions, presents a novel of new integral operator, and discusses the properties of third-order differential subordination. The properties and results of the differential subordination are symmetrical to the properties of the differential superordination to form the sandwich theorems.