Strong Convergence of Approximated Sequences for Nonexpansive Mappings in Banach Spaces
نویسندگان
چکیده
In this paper, we study the convergence of the sequence defined by x0 ∈ C, xn+1 = αnx + (1− αn)Txn, n = 0, 1, 2, . . . , where 0 ≤ αn ≤ 1 and T is a nonexpansive mapping from a closed convex subset of a Banach space into itself.
منابع مشابه
Convergence theorems of multi-step iterative algorithm with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces
The purpose of this paper is to study and give the necessary andsufficient condition of strong convergence of the multi-step iterative algorithmwith errors for a finite family of generalized asymptotically quasi-nonexpansivemappings to converge to common fixed points in Banach spaces. Our resultsextend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8,11, 14, 19]).
متن کاملA 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 کاملStrong Convergence of the Iterations of Quasi $phi$-nonexpansive Mappings and its Applications in Banach Spaces
In this paper, we study the iterations of quasi $phi$-nonexpansive mappings and its applications in Banach spaces. At the first, we prove strong convergence of the sequence generated by the hybrid proximal point method to a common fixed point of a family of quasi $phi$-nonexpansive mappings. Then, we give applications of our main results in equilibrium problems.
متن کاملStrong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings
In this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regular asymptotically nonexpansive mappings in a real reflexive Banach space with a uniformly G$hat{a}$teaux differentiable norm. Our result is applicable in $L_{p}(ell_{p})$ spaces, $1 < p
متن کاملNew hybrid method for equilibrium problems and relatively nonexpansive mappings in Banach spaces
In this paper, applying hybrid projection method, a new modified Ishikawa iteration scheme is presented for finding a common element of the solution set of an equilibrium problem and the set of fixed points of relatively nonexpansive mappings in Banach spaces. A numerical example is given and the numerical behaviour of the sequences generated by this algorithm is compared with several existence...
متن کاملConvergence results: A new type iteration scheme for two asymptotically nonexpansive mappings in uniformly convex Banach spaces
In this article, we introduce a new type iterative scheme for approximating common fixed points of two asymptotically nonexpansive mappings is defined, and weak and strong convergence theorem are proved for the new iterative scheme in a uniformly convex Banach space. The results obtained in this article represent an extension as well as refinement of previous known resu...
متن کامل