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AIMS Mathematics

2023, Volume 8, Issue 1: 841-872. doi: 10.3934/math.2023041
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Equivalence of novel IH-implicit fixed point algorithms for a general class of contractive maps

  • 1.
    Department of Mathematics, Micheal Okpara University of Agriculture, Umudike, Umuahia Abia State Nigeria
  • 2.
    Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore, Pakistan
  • 3.
    Department of Mathematics, University of Management and Technology, Lahore, Pakistan
  • 4.
    Department of Mathematics, Cankaya University, Ankara, Turkey
  • 5.
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
  • Received: 20 July 2022 Revised: 19 September 2022 Accepted: 26 September 2022 Published: 12 October 2022

  • MSC : 47H09, 47H10, 47J05, 65J15

  • In this paper, a novel implicit IH-multistep fixed point algorithm and convergence result for a general class of contractive maps is introduced without any imposition of the "sum conditions" on the countably finite family of the iteration parameters. Furthermore, it is shown that the convergence of the proposed iteration scheme is equivalent to some other implicit IH-type iterative schemes (e.g., implicit IH-Noor, implicit IH-Ishikawa and implicit IH-Mann) for the same class of maps. Also, some numerical examples are given to illustrate that the equivalence is true. Our results complement, improve and unify several equivalent results recently announced in literature.

    Citation: Imo Kalu Agwu, Umar Ishtiaq, Naeem Saleem, Donatus Ikechi Igbokwe, Fahd Jarad. Equivalence of novel IH-implicit fixed point algorithms for a general class of contractive maps[J]. AIMS Mathematics, 2023, 8(1): 841-872. doi: 10.3934/math.2023041

    Related Papers:

  • In this paper, a novel implicit IH-multistep fixed point algorithm and convergence result for a general class of contractive maps is introduced without any imposition of the "sum conditions" on the countably finite family of the iteration parameters. Furthermore, it is shown that the convergence of the proposed iteration scheme is equivalent to some other implicit IH-type iterative schemes (e.g., implicit IH-Noor, implicit IH-Ishikawa and implicit IH-Mann) for the same class of maps. Also, some numerical examples are given to illustrate that the equivalence is true. Our results complement, improve and unify several equivalent results recently announced in literature.


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  • © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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