Applying faster algorithm for obtaining convergence, stability, and data dependence results with application to functional-integral equations

Hasanen A. Hammad; Habib Ur Rehman; Mohra Zayed; Hasanen A. Hammad; Habib Ur Rehman; Mohra Zayed

doi:10.3934/math.20221046

AIMS Mathematics

2022, Volume 7, Issue 10: 19026-19056. doi: 10.3934/math.20221046

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Research article Special Issues

Applying faster algorithm for obtaining convergence, stability, and data dependence results with application to functional-integral equations

1.
Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
3.
Department of Mathematics, Monglkut's University of Technology, Bangkok 10140, Thailand
4.
Mathematics Department, College of Science, King Khalid University, Abha, Saudi Arabia

Received: 21 July 2022 Revised: 19 August 2022 Accepted: 22 August 2022 Published: 29 August 2022
MSC : 47H10, 47A56, 65R20

The goal of this manuscript is to create a new faster iterative algorithm than the previous writing's sober algorithms. In the setting of Banach spaces, this algorithm is used to analyze convergence, stability, and data-dependence results. Basic numerical examples are also provided to highlight the behavior and effectiveness of our approach. Ultimately, the proposed approach is used to solve the functional Volterra-Fredholm integral problem as an application.
- convergence result,
- fixed point,
- data-dependent result,
- $ \Xi $-stable,
- numerical experiment,
- functional integral equation
Citation: Hasanen A. Hammad, Habib Ur Rehman, Mohra Zayed. Applying faster algorithm for obtaining convergence, stability, and data dependence results with application to functional-integral equations[J]. AIMS Mathematics, 2022, 7(10): 19026-19056. doi: 10.3934/math.20221046

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Abstract

The goal of this manuscript is to create a new faster iterative algorithm than the previous writing's sober algorithms. In the setting of Banach spaces, this algorithm is used to analyze convergence, stability, and data-dependence results. Basic numerical examples are also provided to highlight the behavior and effectiveness of our approach. Ultimately, the proposed approach is used to solve the functional Volterra-Fredholm integral problem as an application.

References

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