Proceedings of the 5th International Conference on Statistics, Mathematics, Teaching, and Research 2023 (ICSMTR 2023)

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Approximating Fixed Point of Weak Contraction Mapping Using General Picard-Mann Iteration Process

Authors
Ahmad Ansar1, *, Syamsuddin Mas’ud2
1Department of Mathematics, Universitas Sulawesi Barat, Kabupaten Majene, Indonesia
2Department of Mathematics, Universitas Negeri Makassar, Makassar, Indonesia
*Corresponding author. Email: ahmad.ansar@unsulbar.ac.id
Corresponding Author
Ahmad Ansar
Available Online 18 December 2023.
DOI
10.2991/978-94-6463-332-0_4How to use a DOI?
Keywords
Fixed Point; Weak Contraction; General Picard-Mann
Abstract

Fixed point theory plays a crucial role in solved real world problems in terms of nonlinear problems or differential equations for a suitable mapping. In numerous problems, it is difficult to find an exact fixed point for some contractions mapping. Hence, it is necessary to develop numerical algorithm to approximating the fixed point of contractions mapping. The aim of this article is to study the estimation of fixed point of weak contraction mapping via General Picard Mann (GPM) algorithm. This iteration process is combined Picard and Mann iterative scheme and generalized by making k iteration of that combination. In this research, we prove that the sequences that generated by GPM iterative scheme convergent strongly to unique fixed for weak contractions mapping in uniformly convex Banach spaces. We also prove that GPM algorithm is converge to fixed point faster than any other well-known iteration processes. We compare GPM iterative methods to six other iterative methods related to speed of convergence Finally, we give numerical results for find fixed point of weak contraction mapping using GMP iteration with k = 3 and k = 5 and compare with others under different number of parameters and different function.

Copyright
© 2023 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title
Proceedings of the 5th International Conference on Statistics, Mathematics, Teaching, and Research 2023 (ICSMTR 2023)
Series
Advances in Computer Science Research
Publication Date
18 December 2023
ISBN
10.2991/978-94-6463-332-0_4
ISSN
2352-538X
DOI
10.2991/978-94-6463-332-0_4How to use a DOI?
Copyright
© 2023 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Ahmad Ansar
AU  - Syamsuddin Mas’ud
PY  - 2023
DA  - 2023/12/18
TI  - Approximating Fixed Point of Weak Contraction Mapping Using General Picard-Mann Iteration Process
BT  - Proceedings of the 5th International Conference on Statistics, Mathematics, Teaching, and Research 2023 (ICSMTR 2023)
PB  - Atlantis Press
SP  - 23
EP  - 32
SN  - 2352-538X
UR  - https://doi.org/10.2991/978-94-6463-332-0_4
DO  - 10.2991/978-94-6463-332-0_4
ID  - Ansar2023
ER  -