A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings
نویسندگان
چکیده
Let X be a real Banach space, C a nonempty closed convex subset of X, and T : C → C a mapping. Recall that T is nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖ for all x, y ∈ C. Let Ti : C → C, i 1, 2, . . . , r, be nonexpansive mappings. Let Fix Ti denote the fixed points set of Ti, that is, Fix Ti : {x ∈ C : Tix x}, and let F : ⋂r i 1Fix Ti . For a given x1 ∈ C, and a fixed r ∈ N N denote the set of all positive integers , compute the iterative sequences {x 0 n }, {x 1 n }, {x 2 n }, . . . , {x r n } by
منابع مشابه
A new approximation method for common fixed points of a finite family of nonexpansive non-self mappings in Banach spaces
In this paper, we introduce a new iterative scheme to approximate a common fixed point for a finite family of nonexpansive non-self mappings. Strong convergence theorems of the proposed iteration in Banach spaces.
متن کاملCommon fixed points of a finite family of multivalued quasi-nonexpansive mappings in uniformly convex Banach spaces
In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.
متن کاملStrong convergence of variational inequality problem Over the set of common fixed points of a family of demi-contractive mappings
In this paper, by using the viscosity iterative method and the hybrid steepest-descent method, we present a new algorithm for solving the variational inequality problem. The sequence generated by this algorithm is strong convergence to a common element of the set of common zero points of a finite family of inverse strongly monotone operators and the set of common fixed points of a finite family...
متن کاملA new one-step iterative process for approximating common fixed points of a countable family of quasi-nonexpansive multi-valued mappings in CAT(0) spaces
In this paper, we propose a new one-step iterative process for a countable family of quasi-nonexpansive multi-valued mappings in a CAT(0) space. We also prove strong and $Delta$-convergence theorems of the proposed iterative process under some control conditions. Our main results extend and generalize many results in the literature.
متن کاملApproximating fixed points for nonexpansive mappings and generalized mixed equilibrium problems in Banach spaces
We introduce a new iterative scheme for nding a common elementof the solutions set of a generalized mixed equilibrium problem and the xedpoints set of an innitely countable family of nonexpansive mappings in a Banachspace setting. Strong convergence theorems of the proposed iterative scheme arealso established by the generalized projection method. Our results generalize thecorresponding results...
متن کاملIterative methods for finding nearest common fixed points of a countable family of quasi-Lipschitzian mappings
We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2009 شماره
صفحات -
تاریخ انتشار 2009