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Strong convergence for $\alpha$-nonexpansive mapping using a partial order induced by a function | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 202، دوره 13، شماره 2، مهر 2022، صفحه 2503-2508 اصل مقاله (317.04 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.22013.2314 | ||
| نویسنده | ||
| Reena Jain* | ||
| School of Advanced Sciences and Languages, VIT Bhopal University, India | ||
| تاریخ دریافت: 14 آذر 1399، تاریخ پذیرش: 22 خرداد 1400 | ||
| چکیده | ||
| In this work, we introduce a partial ordering on a Banach space induced by a real valued function and prove some convergence theorems for $\alpha$-nonexpansive mapping in a ordered Banach space to a fixed point of mapping using this partial ordering. Moreover we give example to furnish the definition of the partial ordering induced by a real valued function. | ||
| کلیدواژه‌ها | ||
| $alpha$-nonexpansive mapping؛ Strong Convergence؛ Partial order؛ Fixed point | ||
| مراجع | ||
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[1] B. Abdullatif and A. Khamsi, Mann iteration process for monotone nonexpansive mappings, Fixed Point Theory Appl. 2015 (2015), 177. [2] K. Aoyama and F. Kohsaka, Fixed point theorem for α-nonexpansive mappings in Banach spaces, Nonlinear Anal. 74 (2011), no. 13, 4387–4391. [3] J. Borwein, S. Reich and I. Shafrir, Krasnoselskii Mann iterations in normed spaces, Canad. Math. Bull. 35 (1992), 21–28. [4] F.E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. USA 54 (1965), 1041–1044. [5] K. Goebel and W.A. Kirk, Topics in metric fixed point theory, Cambridge Stud. Adv. Math., vol. 28. Cambridge University Press, Cambridge, 1990. [6] K. Goebel and S. Reich, Uniform convexity, hyperbolic geometry, and nonexpansive mappings, Dekker, New York, 1984. [7] D. G¨ohde, Zum prinzip der kontraktiven abbildung. Math. Nachr. 30 (1965), 251–258. [8] S. Ishikawa, Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65–71. [9] M.A. Khamsi and W.A. Kirk, An introduction to metric spaces and fixed point theory, Wiley, New York, 2001. [10] W.A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Month. 72 (1965), 1004–1006. [11] K. Muangchoo, D. Thongtha, P. Kuman and Y. Je, Fixed point theorems and convergence theorems for monotone (α, β)-nonexpansive mappings in ordered Banach spaces, Creat. Math. Inf. 26 (2017), no. 2, 163–180. [12] J.J. Nieto and R. Rodr´ıguez-L´opez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005), 223–239. [13] A.C.M. Ran and M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Am. Math. Soc. 132 (2004), 1435–1443. [14] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Aust. Math. Soc. 43 (1991), 153–159. [15] R. Shukla, R. Pant and M. Sen, Generalized α-nonexpansive mappings in Banach spaces, Fixed Point Theory Appl. 2017 (2017), 4. | ||
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