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Some New Results on Convergence, Weak w 2 -Stability and Data Dependence of Two Multivalued Almost Contractive Mappings in Hyperbolic Spaces

Author

Listed:
  • Austine Efut Ofem

    (School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4001, South Africa)

  • Jacob Ashiwere Abuchu

    (School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4001, South Africa
    Department of Mathematics, University of Calabar, Calabar P.M.B. 1115, Nigeria)

  • Reny George

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia)

  • Godwin Chidi Ugwunnadi

    (Department of Mathematics, University of Eswatini, Private Bag 4, Kwaluseni M201, Eswatini
    Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria 0204, South Africa)

  • Ojen Kumar Narain

    (School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4001, South Africa)

Abstract

In this article, we introduce a new mixed-type iterative algorithm for approximation of common fixed points of two multivalued almost contractive mappings and two multivalued mappings satisfying condition ( E ) in hyperbolic spaces. We consider new concepts of weak w 2 -stability and data dependence results involving two multivalued almost contractive mappings. We provide examples of multivalued almost contractive mappings to show the advantage of our new iterative algorithm over some exiting iterative algorithms. Moreover, we prove several strong ∆-convergence theorems of our new algorithm in hyperbolic spaces. Furthermore, with another novel example, we carry out a numerical experiment to compare the efficiency and applicability of a new iterative algorithm with several leading iterative algorithms. The results in this article extend and improve several existing results from the setting of linear and CAT(0) spaces to hyperbolic spaces. Our main results also extend several existing results from the setting of single-valued mappings to the setting of multivalued mappings.

Suggested Citation

  • Austine Efut Ofem & Jacob Ashiwere Abuchu & Reny George & Godwin Chidi Ugwunnadi & Ojen Kumar Narain, 2022. "Some New Results on Convergence, Weak w 2 -Stability and Data Dependence of Two Multivalued Almost Contractive Mappings in Hyperbolic Spaces," Mathematics, MDPI, vol. 10(20), pages 1-26, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3720-:d:938472
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    References listed on IDEAS

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    1. Thakur, Balwant Singh & Thakur, Dipti & Postolache, Mihai, 2016. "A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 147-155.
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