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

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  • Keten Çopur, Ayşegül
  • Hacıoğlu, Emirhan
  • Gürsoy, Faik

Abstract

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.

Suggested Citation

  • Keten Çopur, Ayşegül & Hacıoğlu, Emirhan & Gürsoy, Faik, 2024. "New insights on a pair of quasi-contractive operators in Banach spaces: Results on Jungck type iteration algorithms and proposed open problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 476-497.
    • Handle: RePEc:eee:matcom:v:215:y:2024:i:c:p:476-497
    DOI: 10.1016/j.matcom.2023.08.026
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    References listed on IDEAS

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    1. Nawab Hussain & Vivek Kumar & Marwan A. Kutbi, 2013. "On Rate of Convergence of Jungck-Type Iterative Schemes," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-15, May.
    2. Ariza-Ruiz, D. & Garcia-Falset, J., 2015. "Iterative approximation to a coincidence point of two mappings," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 762-776.
    3. S. L. Singh & Charu Bhatnagar & S. N. Mishra, 2005. "Stability of Jungck-type iterative procedures," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-9, January.
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