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Convergence of a new three-step iteration process to common fixed points of three G-nonexpansive mappings in Banach spaces with directed graphs

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Abstract

In this paper, from some confusions in examples on the convergence of certain iteration processes in the literature, we introduce the coordinate-convexity to study the convergence of a new three-step iteration process in Banach spaces with directed graphs. We prove some comparison results of the rate of convergence of the proposed iteration process and certain iteration processes for G-contractive mappings. We also prove the weak and strong convergence results for three G-nonexpansive mappings, and give three numerical examples to illustrate the obtained results.

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Acknowledgements

The authors sincerely thank the anonymous referees for several helpful comments, especially in using Definition 2.12 for the revision of Berinde’s comparison. The authors also thank members of The Dong Thap Group of Mathematical Analysis and its Applications for their discussions on the manuscript. The work is supported by the project SPD2018.01.28 of Dong Thap University, Vietnam.

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Correspondence to Nguyen Trung Hieu.

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Van Dung, N., Trung Hieu, N. Convergence of a new three-step iteration process to common fixed points of three G-nonexpansive mappings in Banach spaces with directed graphs. RACSAM 114, 140 (2020). https://doi.org/10.1007/s13398-020-00872-w

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