A class of Multivalent Meromorphic Functions Involving an Integral Operator

Saleh, Zeinab M; Moustafa, Adela Othman; Madian, Samar Mohamed

doi:10.21608/jfca.2024.290678.1104

A class of Multivalent Meromorphic Functions Involving an Integral Operator

Document Type : Letters to the editor

Authors

¹ Basic Science Dept. Higher. Tec. Instit, The tenth of Ramadan, Egypt.

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

³ Higher Institute of Engineering and Technology New Damietta, Egypt.

10.21608/jfca.2024.290678.1104

Abstract

In this paper, for analytic and multivalent functions defined in the punched disc U^{∗}={ϑ∈ℂ:0<|ϑ-δ|<1}=U\{δ}, δ be a fixed point in U. We define the new class of multivalent meromorphic Bazilevič functions M_{δ,p}^{m}(α,β,μ,ρ,γ) associated with the new integral operator J_{δ,p}^{m}(μ,α), from which one can obtain many other new operators using the principle of Hadamard product (or convolution) by taking different values of its parameters. Let P_{k}(ρ,p) be the class of functions θ(ϑ) analytic in U satisfying θ(0)=p and ∫₀^{2π}|((ℜ{θ(ϑ)}-ρ)/(p-ρ))|dθ≤kπ, where ϑ=re^{iθ},k≥2 and 0≤ρ4 and Aouf and Seoudy 1, we prove our theorems.

Keywords

Main Subjects