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Research Article | Open Access

Common fixed points and convergence results for α-Krasnosel'skii mappings

Amit Gangwar1, Anita Tomar2, Mohammad Sajid3( ), R.C. Dimri1
H.N.B. Garhwal University, Srinagar-246174, Uttarakhand, India
Pt. L.M.S. Campus, Sridev Suman Uttarakhand University, Rishikesh-249201, Uttarakhand, India
Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 51452, Saudi Arabia
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Abstract

We present convergence and common fixed point conclusions of the Krasnosel'skii iteration which is one of the iterative methods associated with α-Krasnosel'skii mappings satisfying condition (E). Our conclusions extend, generalize and improve numerous conclusions existing in the literature. Examples are given to support our results.

Keywords

α-Krasnosel'skii iterationapproximationasymptotically regulariterative methodsmetric projectionSchauder theoremuniformly convex Banach space
CLC number: 47H09, 47H10

References

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AIMS Mathematics
Volume 8 Issue 4,
April 2023
Pages 9911-9923
DOI: 10.3934/math.2023501

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Cite this article:
Gangwar A, Tomar A, Sajid M, et al. Common fixed points and convergence results for α-Krasnosel'skii mappings. AIMS Mathematics, 2023, 8(4): 9911-9923. https://doi.org/10.3934/math.2023501

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Received: 09 January 2023
Revised: 15 February 2023
Accepted: 16 February 2023
Published: 15 April 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)