Certain Families of Holomorphic and Sălăgean Type Bi-Univalent Functions Defined by (p,q)-Lucas Polynomials Involving a Modified Sigmoid Activation Function

Ali Mohammed  Ramadhan; and Najah  Ali Jiben Al-Ziadi

doi:10.24297/jam.v21i.9253

Authors

Ali Mohammed Ramadhan Department of Mathematics, College of Education, University of Al-Qadisiyah, Diwaniya-Iraq
and Najah Ali Jiben Al-Ziadi Department of Mathematics, College of Education, University of Al-Qadisiyah, Diwaniya-Iraq

DOI:

https://doi.org/10.24297/jam.v21i.9253

Keywords:

modified sigmoid function, Sălăgean operator, Lucas polynomials, Fekete-Szegӧ inequality, Bi-univalent functions, Holomorphic function

Abstract

The aim of the present paper is to introduce a certain families of holomorphic and Sălăgean type bi-univalent functions by making use (p, q) - Lucas polynomials involving the modified sigmoid activation function Φ(δ)=z/(1+e^-δ) δ>=1 in the open unit disk Λ. For functions belonging to these subclasses, we obtain upper bounds for the second and third coefficients. Also, we debate Fekete-Szegö inequality for these families. Further, we point out several certain special cases for our results.

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