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Some properties of generalized fundamentally nonexpansive mappings in Banach spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 1343-1352 اصل مقاله (342.78 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.19290.2070 | ||
| نویسنده | ||
| Mohammad Moosaei* | ||
| Department of Mathematics, Faculty of Basic Sciences, Bu-Ali Sina University, Hamedan, Iran | ||
| تاریخ دریافت: 21 آذر 1398، تاریخ پذیرش: 07 مهر 1399 | ||
| چکیده | ||
| In this paper, we introduce a condition on mappings and show that the class of these mappings is broader than both the class of mappings satisfying condition (C) and the class of fundamentally nonexpansive mappings, and it is incomparable with the class of quasi-nonexpansive mappings and the class of mappings satisfying condition (L). Furthermore, we present some convergence theorems and fixed point theorems for mappings satisfying the condition in the setting of Banach spaces. Finally, an example is given to support the usefulness of our results. | ||
| کلیدواژهها | ||
| Fixed point؛ fundamentally nonexpansive mappings؛ generalized nonexpansive mappings؛ Opial's condition؛ quasi-nonexpansive mappings؛ uniformly convex in every direction Banach spaces؛ weakly compact | ||
| مراجع | ||
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s [1] R. P. Agarwal, D. O’Regan and D. R. Sahu, Fixed Point Theory for Lipschitzian-Type Mappings with Applications, Springer, New York, 2009. [2] S. Dhompongsa and N. Nanan, Fixed point theorems by ways of ultra-asymptotic centers, Abst. Appl. Anal. 2011 (2011) Article ID 826851. [3] K. Goebel and W. A. Kirk, Iteration processes for nonexpansive mappings, Contemp. Math. 21 (1983) 115–123. [4] J. Gar´ca-Falset, E. Llorens-Fuster and T. Suzuki, Fixed point theory for a class of generalized of nonexpansive mappings, J. Math. Anal. Appl. 375 (2011) 115–123. [5] E. Llorens-Fuster and E. Moreno-G´alvez, The fixed point theory for some generalized nonexpansive mappings, Abst. Appl. Anal. 2011 (2011) Article ID 435686. [6] M. Moosaei, On fixed point of fundamentally nonexpansive mappings in Banach spaces, Int. J. Nonlinear Anal. Appl. 7(1) (2016) 219–224. [7] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1976) 591–597. [8] T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. 340 (2008) 1088–10 | ||
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