Some Conditions for Certain Two Families of Analytic Functions Associated with Touchard Polynomials

Authors

  • Tariq Al-hawary Department of Applied Science, Ajloun College, Al Balqa Applied University, Ajloun 26816. Jordan
  • Basem Aref Frasin Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq 25113, Jordan
  • Luminita-Ioana Cotˆırl˘a Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
  • Daniel Breaz Department of Mathematics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, 13 Romania

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6182

Keywords:

Analytic, univalent, Touchard polynomials, Poisson distribution, Geometric functions

Abstract

This paper examines necessary and sufficient conditions for the function vs (z), Λ(s, v, z)B using coefficients of Touchard polynomials to be in the classes Q(δ, ζ) and K(δ, ζ) of analytic functions. Furthermore, we estimate certain inclusion relations between the classes Rτ (A1,A2) and K(δ, ζ). Finally, we give a necessary and sufficient condition for an integral operator J vs (z)  to be in the class K(δ, ζ). Special cases for the classes of starlike and convex functions is also considered.

Downloads

Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Complex Analysis

License

Copyright (c) 2025 Tariq Al-hawary, Basem Aref Frasin, Luminita-Ioana Cotˆırl˘a, Daniel Breaz

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Some Conditions for Certain Two Families of Analytic Functions Associated with Touchard Polynomials. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6182. https://doi.org/10.29020/nybg.ejpam.v18i4.6182