Class of Meromorphic Functions Related to New Operator

Yehia, A. M.; Madian, S. M.; Tharwat, M. M.

doi:10.21608/ejmaa.2024.263684.1120

Class of Meromorphic Functions Related to New Operator

Document Type : Regular research papers

Authors

¹ Mathematics and Computer Science, Faculty of Science, Bani Suif University, Bani Suif, Egypt.

² Basic Science Dept. Higher, Instit. Eng. Tec., New Damietta, Egypt.

³ Dept. of Math. and Computer Sci., Faculty of Science, Beni Suef University, Egypt

10.21608/ejmaa.2024.263684.1120

Abstract

In this paper, using a meromorphic univalent function of the form f(z)=(1/(z-δ))+∑_{k=j}^{∞} a_{k}(z-δ)^{k}, with missing coefficients which has a simple pole at the point z= δ, 0≤δ<1, that is it is defined in U^{∗}=U\{δ}={z:z∈ℂ and 0<|z-δ|<1}, we note that for δ=0 we obtain the class ∑_{j} of meromorphic functions. We define a new operator analogue of that of Aouf et al. [2] for univalent analytic functions defined in the open unit dick U and introduce new class of meromorphic univalent functions which for different values of its parameters many special new classes can be obtained from it. For this class of functions we obtained some of its properties such as coefficient estimates, distortion theorem, the modified Hadamard product of two functions in it and also for function which its coefficients are the sum of the squares of the coefficients of two functions. Also we obtained analogue results of these results for each of the subclass obtained from this class.

Keywords

Main Subjects