Inclusion Properties for Classes of Univalent Functions

Mowafy, Mohamed; Mostafa, Adela; Madian, Samer

doi:10.21608/ejmaa.2023.220724.1046

Inclusion Properties for Classes of Univalent Functions

Document Type : Regular research papers

Authors

¹ Mathematical Department, Faculty of Science, Mansoura University, Egypt

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

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

10.21608/ejmaa.2023.220724.1046

Abstract

In this paper, using operator Mowafy et. al. Which modified the operator of Al-Aboudi and Al-Amoudi we defined a new operator from which one can obtain many other new operators using the principle of Hadamard product (or convolution) by taking different values of its parameters. This operator has, three recurrence relations. Using one of its these recurrence relation we defined four classes related to univalent starlike and convex functions of order α, close-to-convex and quasi-convex functions of order η and type α ( 0≤α,η<1), which in turn generalize many other classes for different values of parameter. For these classes and by using Miller and Mocanu lemma we can obtain many inclusion results. Also some inclusion resulls for Libera integral operator are obtained. We have proved our rersults here by using the first recurrence relation. Using similar argument by applying the second and third recurrence relation one can get new results.

Keywords