Further generalizations of the Ishikawa algorithm

Mohammad Reza Haddadi; Vahid Parvaneh; Monica Bota; Mohammad Reza Haddadi; Vahid Parvaneh; Monica Bota

doi:10.3934/math.2023614

AIMS Mathematics

2023, Volume 8, Issue 5: 12185-12194. doi: 10.3934/math.2023614

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Further generalizations of the Ishikawa algorithm

1.
Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
2.
Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran
3.
Department of Mathematics, Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca, Romania

Received: 27 October 2022 Revised: 06 March 2023 Accepted: 08 March 2023 Published: 22 March 2023
MSC : 90C48, 47H09, 46B20

We provide an iterative algorithm for fixed point issues in vector spaces in the paragraphs that follow. We demonstrate that, compared to the Ishikawa technique in Banach spaces, the iterative algorithm presented in this study performs better under weaker conditions. In order to achieve this, we compare the convergence behavior of iterations, and taking into account a few offered cases, we support the major findings.
- best proximity point,
- fixed point,
- uniformly convex Banach space,
- iterative sequence
Citation: Mohammad Reza Haddadi, Vahid Parvaneh, Monica Bota. Further generalizations of the Ishikawa algorithm[J]. AIMS Mathematics, 2023, 8(5): 12185-12194. doi: 10.3934/math.2023614

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Abstract

We provide an iterative algorithm for fixed point issues in vector spaces in the paragraphs that follow. We demonstrate that, compared to the Ishikawa technique in Banach spaces, the iterative algorithm presented in this study performs better under weaker conditions. In order to achieve this, we compare the convergence behavior of iterations, and taking into account a few offered cases, we support the major findings.

References

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