Convolution Results for Subclasses of Multivalent Meromorphic Functions of Complex Order Involving an Integral Operator

Saleh, Zeinab M.; Mostafa, Adela O.; Madian, Samer M.

doi:10.21608/ejmaa.2025.355261.1315

Convolution Results for Subclasses of Multivalent Meromorphic Functions of Complex Order Involving an Integral Operator

Document Type : Regular research papers

Authors

¹ Higher Technological Institute in the tenth of Ramadan

² Math. Dept., Faculty of Science, Mansoura University

³ Basic Science Dept., Higher Institute for, Engineering and Technology, New Damietta, Egypt

10.21608/ejmaa.2025.355261.1315

Abstract

In the paper, we will define a new integral operator of meromorphic p-valent functions, by using this operator we introduce subclasses of meromorphic p-valent functions. And if we take different values for this operator, we will get new classes of meromorphic p-valent functions.The integral operator J_{p}^{m}(μ,α) is a specific integral transform used in mathematical analysis, particularly in connection with solving certain differential equations and studying properties of functions. The study of Multivalent Meromorphic functions in connection with the integral operator J_{p}^{m}(μ,α) involves analyzing how the operator affects the analytic properties of functions, ensuring convergence, and understanding the behavior. These properties are crucial for applications in various branches of mathematics, including differential equations, harmonic analysis, and integral transforms. This paper aims to investigate convolution properties, coefficient estimates and containment properties for these subclasses with the integral operator J_{p}^{m}(μ,α) within U^{∗}={ϑ∈ℂ:0<|ϑ|<1}=U\{δ}. We will establish fundamental properties such as coefficient inequalities, integral means inequalities and subordination results for these subclasses.

Keywords