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Fixed points and common points for fundamentally nonexpansive mappings on banach spaces | ||
Journal of Hyperstructures | ||
دوره 4، شماره 1، شهریور 2015، صفحه 50-56 اصل مقاله (83.4 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22098/jhs.2015.2597 | ||
نویسنده | ||
Moohammad Moosaei* | ||
Department of Mathematics, Faculty of Science, Bu-Ali Sina University, P.O.Box 6517838695, Hamedan, Iran | ||
چکیده | ||
In this paper, we present some fixed point theorems for fundamentally nonexpansive mappings in Banach spaces and give one common fixed point theorem for a commutative family of demiclosed fundamentally nonexpansive mappings on a nonempty weakly compact convex subset of a strictly convex Banach space with the Opial condition and a uniformly convex in every direction Banach space, respectively; moreover, we show that the common fixed points set of such a family of mappings is closed and convex. | ||
کلیدواژهها | ||
Common fixed point؛ Fixed point؛ Fundamentally nonexpansive mappings؛ nonexpansive mappings؛ Opial’s condition؛ Uniformly convex in every direction Banach spaces | ||
مراجع | ||
[1] R. P. Agarwal, D. O’Regan and D. R. Sahu, Fixed Point Theory for Lipschitzian-Type Mappings with Applications, Springer, Heidelberg (2003). [2] D. van Dulst, Equivalent norms and the fixed point property for nonexpansive mappings, J. London Math. Soc. 25 (1982), 139-144. [3] K. Goebel and W. A. Kirk, Iteration processes for nonexpansive mappings, Con-temp. Math. 21 (1983), 115-123. [4] S. J. Hosseini Ghoncheh and A. Razani, Fixed point theorems for some general-ized nonexpansive mappings in ptolemy spaces, Fixed Point Theory Appl. 2014 (2014). [5] S. Ishikawa, Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65-71. [6] M. Moosaei, On fixed points of fundamentally nonexpansive mappings in Banach spaces, Int. J. Nonlinear Anal. Appl (to appear). [7] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1976), 591-597. [8] W. Rudin, Functional Analysis, 2nd ed., McGraw-Hill, New York (1991). [9] T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. 340 (2008), 1088-1095. [10] T. Suzuki, Strongly convergence theorems for infinite families of nonexpansive mappings in general Banach spaces, Fixed Point Theory Appl. 2005 (2005), 103-123. | ||
آمار تعداد مشاهده مقاله: 35 تعداد دریافت فایل اصل مقاله: 59 |