Coefficient bounds for Al-Oboudi type bi-univalent functions connected with a modified sigmoid activation function and \(k\)-Fibonacci numbers

Volume 27, Issue 2, pp 105--117 http://dx.doi.org/10.22436/jmcs.027.02.02

Publication Date: April 13, 2022 Submission Date: December 08, 2021 Revision Date: December 21, 2021 Accteptance Date: January 15, 2022

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Authors

A. Amourah - Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid, Jordan. B. A. Frasin - Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq, Jordan. S. R. Swamy - Department of Computer Science and Engineering, RV College of Engineering, Bengaluru, 560 059, Karnataka, India. Y. Sailaja - Department of Mathematics, RV College of Engineering, Bengaluru, 560 059, Karnataka, India.

Abstract

Using the Al-Oboudi type operator, we present and investigate two special families of bi-univalent functions connected with the activation function \(% \phi (s)=\ 2/(1+e^{-s}),\,s\in \mathbb{R}\) and \(k\)-Fibonacci numbers. We derive the bounds on initial coefficients and the Fekete-Szego functional for functions of the type \(g_{\phi }(z)=z+\sum \limits_{j=2}^{\infty }\phi (s)d_{j}z^{j}\) in these introduced families. Furthermore, we present interesting observations of the results investigated.

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Keywords

• Fekete-Szego inequality
• regular function
• Sigmoid function
• Fibonacci numbers
• bi-univalent function

MSC

•  30C45
•  11B65

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