New insights on a pair of quasi-contractive operators in Banach spaces: Results on Jungck type iteration algorithms and proposed open problems

In this paper, we explore relationships among the pairs of various well-known contractive type operators in Banach spaces. We also present a novel Jungck type iteration algorithm for a pair of quasi-contractive operators, which is thoroughly investigated in terms of strong convergence, stability, and data dependency. To demonstrate the efficacy of the proposed algorithm and reliability of each of the mentioned results, we furnish illustrative academic examples including both linear and nonlinear DEs. Furthermore, we present several open problems that warrant further study. Our results complement recent findings in the literature and contribute to further development in this area. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.