Equivalence of novel IH-implicit fixed point algorithms for a general class of contractive maps-Reference-Cited by-同舟云学术

Equivalence of novel IH-implicit fixed point algorithms for a general class of contractive maps

Published:2023 Issue:1 Volume:8 Page:841-872
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Agwu Imo Kalu¹,Ishtiaq Umar²,Saleem Naeem³,Igbokwe Donatus Ikechi¹,Jarad Fahd⁴⁵

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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