Estimating fixed points of non-expansive mappings with an application

Mohd Jubair; Faizan Ahmad Khan; Javid Ali; Yeşim Saraç; Mohd Jubair; Faizan Ahmad Khan; Javid Ali; Yeşim Saraç

doi:10.3934/math.2021558

AIMS Mathematics

2021, Volume 6, Issue 9: 9590-9601. doi: 10.3934/math.2021558

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Research article

Estimating fixed points of non-expansive mappings with an application

1.
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2.
Department of Mathematics, Tabuk University, Tabuk, KSA
3.
Department of Mathematics, Ataturk University, Erzurum, Turkey

Received: 16 March 2021 Accepted: 15 June 2021 Published: 25 June 2021
MSC : 47H09, 47H10, 54H25

In this paper, we study a three step iterative scheme to estimate fixed points of non-expansive mappings in the framework of Banach spaces. Further, some convergence results are proved for such mappings. A nontrivial numerical example is presented to verify our assertions and main results. Finally, we approximate the solution of a boundary value problem of second order differential equation.
- fixed points,
- non-expansive mappings,
- iterative schemes,
- uniformly convex Banach space,
- second order ordinary differential equation
Citation: Mohd Jubair, Faizan Ahmad Khan, Javid Ali, Yeşim Saraç. Estimating fixed points of non-expansive mappings with an application[J]. AIMS Mathematics, 2021, 6(9): 9590-9601. doi: 10.3934/math.2021558

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Abstract

In this paper, we study a three step iterative scheme to estimate fixed points of non-expansive mappings in the framework of Banach spaces. Further, some convergence results are proved for such mappings. A nontrivial numerical example is presented to verify our assertions and main results. Finally, we approximate the solution of a boundary value problem of second order differential equation.

References

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