Approximation of fixed point of generalized non-expansive mapping via new faster iterative scheme in metric domain

Noor Muhammad; Ali Asghar; Samina Irum; Ali Akgül; E. M. Khalil; Mustafa Inc; Noor Muhammad; Ali Asghar; Samina Irum; Ali Akgül; E. M. Khalil; Mustafa Inc

doi:10.3934/math.2023149

AIMS Mathematics

2023, Volume 8, Issue 2: 2856-2870. doi: 10.3934/math.2023149

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Research article

Approximation of fixed point of generalized non-expansive mapping via new faster iterative scheme in metric domain

1.
Department of Mathematics and Statistics, Institute of Southern Punjab, Multan, Pakistan
2.
Department of Mathematics, Art and Science faculty, Siirt University, 56100 Siirt, Turkey
3.
Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC 99138, Nicosia/Mersin, Turkey
4.
Department of Mathematics, College of Science, P. O. Box 11099, Taif University, Taif 21944, Saudi Arabia
5.
Department of Mathematics, Science Faculty Firat University, Elazig, Turkey
6.
Department of Medical Research China Medical University, Taichung, Taiwan, China

Received: 31 August 2022 Revised: 26 October 2022 Accepted: 31 October 2022 Published: 10 November 2022
MSC : 47H09, 47H10, 47J25

In this paper, we establish a new iterative process for approximation of fixed points for contraction mappings in closed, convex metric space. We conclude that our iterative method is more accurate and has very fast results from previous remarkable iteration methods like Picard-S, Thakur new, Vatan Two-step and K-iterative process for contraction. Stability of our iteration method and data dependent results for contraction mappings are exact, correspondingly on testing our iterative method is advanced. Finally, we prove enquiring results for some weak and strong convergence theorems of a sequence which is generated from a new iterative method, Suzuki generalized non-expansive mappings with condition $ (C) $ in uniform convexity of metric space. Our results are addition, enlargement over and above generalization for some well-known conclusions with literature for theory of fixed point.
- Suzuki generalized non expansive mapping,
- uniformly convex metric space,
- iteration process,
- weak convergence,
- strong convergence,
- condition $ (C) $
Citation: Noor Muhammad, Ali Asghar, Samina Irum, Ali Akgül, E. M. Khalil, Mustafa Inc. Approximation of fixed point of generalized non-expansive mapping via new faster iterative scheme in metric domain[J]. AIMS Mathematics, 2023, 8(2): 2856-2870. doi: 10.3934/math.2023149

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Abstract

In this paper, we establish a new iterative process for approximation of fixed points for contraction mappings in closed, convex metric space. We conclude that our iterative method is more accurate and has very fast results from previous remarkable iteration methods like Picard-S, Thakur new, Vatan Two-step and K-iterative process for contraction. Stability of our iteration method and data dependent results for contraction mappings are exact, correspondingly on testing our iterative method is advanced. Finally, we prove enquiring results for some weak and strong convergence theorems of a sequence which is generated from a new iterative method, Suzuki generalized non-expansive mappings with condition $ (C) $ in uniform convexity of metric space. Our results are addition, enlargement over and above generalization for some well-known conclusions with literature for theory of fixed point.

References

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