Article
Kyungpook Mathematical Journal 2023; 63(1): 45-60
Published online March 31, 2023
Copyright © Kyungpook Mathematical Journal.
On ϑ -quasi-Geraghty Contractive Mappings and Application to Perturbed Volterra and Hypergeometric Operators
Olalekan Taofeek Wahab
Department of Mathematics and Statistics, Kwara State University, Malete, P. M. B. 1530 Ilorin, Nigeria
e-mail : taofeek.wahab@kwasu.edu.ng
Received: November 30, 2021; Revised: April 25, 2022; Accepted: May 3, 2022
In this paper we suggest an enhanced Geraghty-type contractive mapping for examining the existence properties of classical nonlinear operators with or without prior degenerates. The nonlinear operators are proved to exist with the imposition of the Geraghty-type condition in a non-empty closed subset of complete metric spaces. To showcase some efficacies of the Geraghty-type condition, convergent rate and stability are deduced. The results are used to study some asymptotic properties of perturbed integral and hypergeometric operators. The results also extend and generalize some existing Geraghty-type conditions.
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