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Date Published: 14/06/2020
Online Published: 14/06/2020
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DOI: https://doi.org/10.52714/dthu.9.3.2020.786
Issue
Vol. 9 No. 3 (2020): Natural Sciences Issue (Vietnamese)
Section
Natural Sciences Issue (Vietnamese)
How to Cite
Cao, P. C. T., & Nguyen, T. H. (2020). Convergence of a two-step iteration process to common fixed points of two asymptotically g-nonexpansive mappings in Banach spaces with graphs. Dong Thap University Journal of Science, 9(3), 13-22. https://doi.org/10.52714/dthu.9.3.2020.786

Convergence of a two-step iteration process to common fixed points of two asymptotically g-nonexpansive mappings in Banach spaces with graphs

Pham Cam Tu Cao1, Trung Hieu Nguyen2,
1 Student, Dong Thap University, Vietnam
2 Dong Thap University, Vietnam

Main Article Content

Abstract

In this paper, we introduce a new two-step iteration scheme for two asymptotically G-nonexpansive mappings in uniformly convex Banach spaces with graphs. Wethenprove some weak and strong convergence results to common fixed points of two asymptotically G-nonexpansive mappings in uniformly convex Banach spaces with graphs. These results are the extension of some major results reported by Wattanawweekul (2018). In addition, we give an example to illustrate for the convergence of the introduced iteration process and show that the convergence of this process to common fixed points of two asymptotically G-nonexpansive mappings is faster than those presented by Wattanawweekul (2018).

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Keywords

Asymptotically G-nonexpansive mapping, common fixed point, Banach spaces with graph

References

Dung, N. V., & Hieu, N. T. (2020). Convergence of a new three-step iteration process to common fixed points of three G-nonexpansive mappings in Banach spaces with directed graphs. Rev. R. Acad. Cienc. Exacts Fis. Nat. Ser. A Math. RACSAM, 114(140), 1-24.
Dung, N. V., & Hieu, N. T. (2019). A new hybrid projection algorithm for equilibrium problems and asymptotically quasi -nonexpansive mappings in Banach spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, (3), 2017-2035.
Goebel, K., & Kirk, W. A. (1972). A fixed point theorem for asymptotically nonexpansive mappings. Proc. Amer. Math. Soc., (1), 171-174.
Jachymski, J. (2008). The contraction principle for mappings on a metric space with a graph. Proc. Amer. Math. Soc., (4), 1359-1373.
Sangago, M. G., Hunde, T. W., & Hailu, H. Z. (2018). Demiclodeness and fixed points of G-asymptotically nonexpansive mapping in Banach spaces with graph. Adv. Fixed Point Theory, 8(3), 313-340.
Shahzad, N., & Al-Dubiban, R. (2006). Approximating common fixed points of nonexpansive mappings in Banach spaces.
Suparatulatorn, R., Cholamjiak, W., & Suantai, S. (2018). A modified S-iteration process for G-nonexpansive mappings in Banach spaces with graphs. Numerical Algorithms, 77, 479-490.
Wattanataweekul, M. (2018). Approximating common fixed points for two G- asymptotically nonexpansive mappings with directed graphs. Thai J. Math., (3), 817-830.

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