Approximation of fixed points for a new class of generalized non-expansive mappings in Banach spaces

Thabet Abdeljawad; Nazli Kadioglu Karaca; Isa Yildirim; Aiman Mukheimer; Thabet Abdeljawad; Nazli Kadioglu Karaca; Isa Yildirim; Aiman Mukheimer

doi:10.3934/math.2024584

AIMS Mathematics

2024, Volume 9, Issue 5: 11958-11974. doi: 10.3934/math.2024584

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Research article

Approximation of fixed points for a new class of generalized non-expansive mappings in Banach spaces

1.
Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia
2.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
3.
Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea
4.
Department of Mathematics and Applied Mathematics School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa
5.
Department of Mathematics, Faculty of Science, Ataturk University, Erzurum 25240, Turkey

Received: 16 February 2024 Revised: 17 March 2024 Accepted: 20 March 2024 Published: 27 March 2024
MSC : 47H09, 47H10, 47J25, 54H25

In this paper, we first introduced a new class of generalized non-expansive mappings, which was larger than the class satisfying the condition $ B_{\gamma, \mu } $. Also, we proposed a new iterative process to approximate the fixed point of the mapping we introduced in this work, then we prove convergence theorems for these mappings by using our iteration process. Lastly, a numerical example was given to show the efficiency of this new iteration process. Our results were the extension and generalization of many known results in the literature in fixed point theory.
- fixed point,
- generalized non-expansive mappings,
- uniformly convex Banach space
Citation: Thabet Abdeljawad, Nazli Kadioglu Karaca, Isa Yildirim, Aiman Mukheimer. Approximation of fixed points for a new class of generalized non-expansive mappings in Banach spaces[J]. AIMS Mathematics, 2024, 9(5): 11958-11974. doi: 10.3934/math.2024584

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Abstract

In this paper, we first introduced a new class of generalized non-expansive mappings, which was larger than the class satisfying the condition $ B_{\gamma, \mu } $. Also, we proposed a new iterative process to approximate the fixed point of the mapping we introduced in this work, then we prove convergence theorems for these mappings by using our iteration process. Lastly, a numerical example was given to show the efficiency of this new iteration process. Our results were the extension and generalization of many known results in the literature in fixed point theory.

References

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