Approximation of Common Fixed Points of a Sequence of Nearly Nonexpansive Mappings and Solutions of Variational Inequality Problems (original) (raw)
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Mathematical and Computer Modelling
In this paper, we introduce a new iterative scheme for finding a common element of the set of solutions of a general system of variational inequalities, the set of solutions of a mixed equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a real Hilbert space. Using the demi-closedness principle for nonexpansive mapping, we prove that the iterative sequence converges strongly to a common element of the above three sets under some control conditions. Our main result extends a recent result of Ceng, Wang and Yao [L.C. Ceng, C.Y. Wang and J.C. Yao, Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities, Math. Meth. Oper. Res. 67 (2008) 375-390].
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an inverse strongly monotone mapping in a real Hilbert space. Also, we prove that under quite mild conditions the iterative sequence defined by our new extragradient method converges strongly to a solution of the fixed point problem for an infinite family of nonexpansive mappings and the classical variational inequality problem. In addition, utilizing this result, we provide some applications of the considered problem not just giving a pure extension of existing mathematical problems.
Journal of Applied Mathematics and Computing, 2010
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Applied Mathematics and Computation, 2010
In this paper, we introduce a modified explicit iterative process for finding a common element of the solutions of an equilibrium problem and the set of common fixed points of a finite family of asymptotically k-strictly pseudocontractive mappings in the intermediate sense in the framework of Hilbert spaces. We get a weak convergence theorem for finding a common element of the above two sets and then we modify these algorithms to have a strong convergence theorem by using a hybrid method in the mathematical programming. Our results improve and extend the recent ones announced by many others.
Convergence of a general iterative method for nonexpansive mappings in Hilbert spaces
Journal of Computational and Applied Mathematics, 2009
In this paper, we introduce a modified Ishikawa iterative process for approximating a fixed point of nonexpansive mappings in Hilbert spaces. We establish some strong convergence theorems of the general iteration scheme under some mild conditions. The results improve and extend the corresponding results of many others.
Strong convergence theorems on an iterative method for a family of finite nonexpansive mappings
Applied Mathematics and Computation, 2006
Let E be either a strictly convex and reflexive Banach spaces with a uniformly Gâteaux differentiable norm or a reflexive Banach spaces with a weakly sequentially continuous duality mapping, and K be a nonempty closed convex subset of E. For a family of finite many nonexpansive mappings {T l } (l = 1,2,. . . , N) and fixed contractive mapping f : K ! K, define iteratively a sequence {x n } as follows: