Certain subclasses of analytic functions with complex order associated with generalized Bessel functions

Authors

  • T. Al-Hawary Al-Balqa Applied University, Jordan
  • A. Amourah Irbid National University, Irbid, Jordan
  • M.K. Aouf Mansoura University, Egypt
  • B.A. Frasin Al al-Bayt University, Mafraq, Jordan

DOI:

https://doi.org/10.31926/but.mif.2023.3.65.1.3

Keywords:

analytic functions, Hadamard product, generalized Bessel functions

Abstract

In this paper, we obtain the necessary and sufficient conditions for generalized Bessel functions of the first kind zup(z) to be in the classes S(b, λ, β) and R(b, λ, β) of analytic functions with complex order and also give the necessary and sufficient conditions for z(2−up(z)) to be in the classes TS(b, λ, β) and TR(b, λ, β). Furthermore, we give the necessary and sufficient conditions for J(k, c) to be in the class TR(b, λ, β) provided that the function f is in the class Rτ (A, B). Finally, we give conditions for the integral operator G(k, c, z) = ∫0z(2 − up(t))dt to be in the class TR(b, λ, β). Several corollaries and consequences of the main results are also obtained.

Author Biographies

T. Al-Hawary, Al-Balqa Applied University, Jordan

Department of Applied Science, Ajloun College, Ajloun 26816

A. Amourah, Irbid National University, Irbid, Jordan

Department of Mathematics, Faculty of Science and Technology

M.K. Aouf, Mansoura University, Egypt

Department of Mathematics, Faculty of Science, Mansoura 35516

B.A. Frasin, Al al-Bayt University, Mafraq, Jordan

Faculty of Science, Department of Mathematics

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Published

2023-07-03

Issue

Section

MATHEMATICS