Fixed Point of Total Asymptotically Nonexpansive Mappings in Banach Spaces

Article Sidebar

PDF
Published: Jun 25, 2024
Keywords:
Condition (𝐴) Fixed point Strong convergence Total asymptotically nonexpansive Uniformly convex

Main Article Content

Kannika Khomphurngson
Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand
Kamonrat Nammanee
Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand

Abstract

In this paper, we present a strong convergence theorem for total asymptotically nonexpansive mappings in a real uniformly convex Banach space.

Article Details

How to Cite
Kannika Khomphurngson, & Nammanee, K. (2024). Fixed Point of Total Asymptotically Nonexpansive Mappings in Banach Spaces. Science & Technology Asia, 29(2), 183–190. Retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/249420
Issue
Vol.29 No.2 (April-June 2024)
Section
Physical sciences
Creative Commons License

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

References

Khomphurngson K., Kamyan N., Nammanee K. New modified hybrid algorithm for pseudo-contractive mappings in Hilbert spaces. J. Nonlinear Funct. Anal. 2022; (2022): 25.

Berinde, V., Pcurar, M. Approximating fixed points of enriched contractions in Banach spaces. Fixed Point Theory Appl.2020; 22(2): 1–10. https://doi: 10.1007/s11784-020-0769-9

Deshmukh, A., Gopal, D., Rakocevi, V. Two new iterative schemes to approximate the fixed points for mappings. International Journal of Nonlinear Sciences and Numerical Simulation. 2023; 24(4): 1265-1309. https://doi.org/10.1515/ijnsns-2021-0141

Salisu S., Kumam P., Sriwongsa S., Gopal D. Enriched asymptotically nonexpansive mappings with center zero. Filomat. 2024; 38:1: 343–356.

Goebel K., Kirk WA. A fixed point theorem for asymptotically nonexpansive mappings. Proc. Am. Math. Soc. 1972; 35: 171-174.

Alber YI., Chidume CE., Zegeye H. Approximating fixed points of total asymptotically nonexpansive mappings. Fixed Point Theory Appl. 2006; Article ID 10673.

Onsod W., Kumam P., Saleewong T. Fixed Point of Suzuki-Geraghty Type -Contractions in Partial Metric Spaces with Some Applications. Science & Technology Asia. 2023; 28(1).

Pansuwan A., Sintunavarat W. The new hybrid iterative algorithm for numerical Reckoning fixed point of Suzuki’s generalized nonexpansive mappings with numerical experiments, Thai journal of Mathematics 2021; 19:167-168.

Kaewkhao A., Bussaban L., Suantai S. Convergence Theorem of Inertial Piteration Method for a Family of Nonexpansive Mappings with Applications, Thai J. Math. 2020; 18 (4): 1743-1751.

Khan SH., Fukhar-ud-din H. Approximating fixed points of -nonexpansive mappings by RK-iterative process in modular function spaces, J. Nonlinear Var. Anal. 2019; (3): 107-114.

Budzyska M., Grzesik A., Kaczor W., Kuczumow T. A remark on the fixed point property of nonexpansive mappings, J. Nonlinear Var. Anal. 2018; (2): 35-47.

Marino G., Zaccone R. On strong convergence of some midpoint type methods for nonexpansive mappings, J. Nonlinear Var. Anal. 2017; (1): 159-174.

Chidume CE., Ofoedu EU., Approximation of common fixed points for finite families of total asymptotically nonexpansive mappings. J. Math. Anal. Appl. 2007; 333 (1): 128-141.

Chidume CE., Ofoedu EU. A new iteration process for approximation of common fixed points for finite families of total asymptotically nonexpansive mappings. Int. J. Math. Math. Sci. 2009; Article ID 615107.

Kim GE. Approximating common fixed points for total asymptotically nonexpansive mappings. J. Appl. Math. Inform. 2012; 30: 71 82.

Kim GE. Strong convergence to a fixed point of total asymptotically nonexpansive mappings. Fixed Point Theory Appl. 2013; 2013:302.

Kim GE., Kim TH. Strong convergence theorems of total asymptotically nonexpansive mappings. In: Proceedings of the 7th International Conference on Nonlinear Analysis and Convex Analysis, 2011; pp. 197-208.

Nammanee K. Fixed point iterations for nonexpansive and asymptotically nonexpansive mappings in a Banach space. [Ph.D. thesis]. Phitsanulok: Naresuan University; 2007.

Ishikawa S. Fixed points by a new iteration method, Proc. Amer. Math. Soc. 1974; 44 (1): 147–150.

Mann WR. Mean value methods in iteration, Proc. Amer. Math. Soc. 1953; (4): 506–510.

Rhoades BE. Fixed point iterations for certain nonlinear mappings. J. Math. Anal. Appl. 1994; 183: 118-120.

Schu J. Iterative construction of fixed points of asymptotically nonexpansive mappings. J. Math. Anal. Appl. 1991; 158: 407-413.

Kim GE. Weak and strong convergence of the modified Mann iteration process for nonexpansive mappings. J. Nonlinear Convex Anal. 2012; 13(3): 449-457.

Senter HF., Dotson WG. Approximating fixed points of nonexpansive mappings. Proc. Am. Math. Soc. 1974; 44: 375-380.

Qihou L. Iterative sequences for asymptotically quasi-nonexpansive mappingswith error member. J. Math. Anal. Appl. 2001; 259: 18-24.

Groetsch CW. A note on segmenting Mann iterates. J. Math. Anal. Appl.1972; 40: 369-372.