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A novel three-step implicit iteration process for three finite family of asymptotically generalized Φ-hemicontractive map** in the intermediate sense

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Abstract

In this paper, we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalized Φ-hemicontractive map**s in the intermediate sense. We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalized Φ-hemicontractive map**s in the intermediate sense. Our results extends, improves and complements several known results in literature.

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Acknowledgement

The authors wish to thank the referees for their useful comments and suggestions. This paper was completed while the first author was visiting the Abdus Salam School of Mathematical Sciences (ASSMS), Government College University Lahore, Pakistan as a postdoctoral fellow.

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Authors and Affiliations

  1. Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526, Owerri, Imo State, Nigeria

    Godwin Amechi Okeke

  2. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

    Austine Efut Ofem

  3. Department of Mathematics, University of Uyo, Uyo, Nigeria

    Austine Efut Ofem

Authors
  1. Godwin Amechi Okeke
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  2. Austine Efut Ofem
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Correspondence to Godwin Amechi Okeke or Austine Efut Ofem.

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Conflict of interest The authors declare no conflict of interest.

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Okeke, G.A., Ofem, A.E. A novel three-step implicit iteration process for three finite family of asymptotically generalized Φ-hemicontractive map** in the intermediate sense. Appl. Math. J. Chin. Univ. 38, 248–263 (2023). https://doi.org/10.1007/s11766-023-4228-4

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  • DOI: https://doi.org/10.1007/s11766-023-4228-4

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