The Experts below are selected from a list of 8973 Experts worldwide ranked by ideXlab platform
A Adamu - One of the best experts on this subject based on the ideXlab platform.
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a strong convergence theorem for generalized φ strongly monotone maps with applications
Fixed Point Theory and Applications, 2019Co-Authors: C E Chidume, Monday Ogudu Nnakwe, A AdamuAbstract:Let X be a uniformly convex and uniformly smooth Real Banach Space with dual Space $X^{*}$ . In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-strongly monotone map is constructed. A strong convergence theorem for a sequence generated by the algorithm is proved. Furthermore, the theorem is applied to approximate the solution of a convex optimization problem, a Hammerstein integral equation, and a variational inequality problem. This theorem generalizes, improves, and complements some recent results. Finally, examples of generalized-Φ-strongly monotone maps are constructed and numerical experiments which illustrate the convergence of the sequence generated by our algorithm are presented.
Poom Kumam - One of the best experts on this subject based on the ideXlab platform.
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a hybrid iterative scheme for a maximal monotone operator and two countable families of relatively quasi nonexpansive mappings for generalized mixed equilibrium and variational inequality problems
Abstract and Applied Analysis, 2010Co-Authors: Siwaporn Saewan, Poom KumamAbstract:We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone operator, the set of solutions of the generalized mixed equilibrium problem and zeros of a maximal monotone operator in the framework of a Real Banach Space. We obtain a strong convergence theorem for the sequences generated by this process in a 2 uniformly convex and uniformly smooth Banach Space. The results presented in this paper improve and extend some recent results.
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convergence theorem based on a new hybrid projection method for finding a common solution of generalized equilibrium and variational inequality problems in Banach Spaces
Abstract and Applied Analysis, 2010Co-Authors: Siwaporn Saewan, Poom Kumam, Kriengsak WattanawitoonAbstract:The purpose of this paper is to introduce a new hybrid projection method for finding a common element of the set of common fixed points of two relatively quasi-nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone, and the set of solutions of the generalized equilibrium problem in the framework of a Real Banach Space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach Space. Base on this result, we also get some new and interesting results. The results in this paper generalize, extend, and unify some well-known strong convergence results in the literature.
Siwaporn Saewan - One of the best experts on this subject based on the ideXlab platform.
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a hybrid iterative scheme for a maximal monotone operator and two countable families of relatively quasi nonexpansive mappings for generalized mixed equilibrium and variational inequality problems
Abstract and Applied Analysis, 2010Co-Authors: Siwaporn Saewan, Poom KumamAbstract:We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone operator, the set of solutions of the generalized mixed equilibrium problem and zeros of a maximal monotone operator in the framework of a Real Banach Space. We obtain a strong convergence theorem for the sequences generated by this process in a 2 uniformly convex and uniformly smooth Banach Space. The results presented in this paper improve and extend some recent results.
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convergence theorem based on a new hybrid projection method for finding a common solution of generalized equilibrium and variational inequality problems in Banach Spaces
Abstract and Applied Analysis, 2010Co-Authors: Siwaporn Saewan, Poom Kumam, Kriengsak WattanawitoonAbstract:The purpose of this paper is to introduce a new hybrid projection method for finding a common element of the set of common fixed points of two relatively quasi-nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone, and the set of solutions of the generalized equilibrium problem in the framework of a Real Banach Space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach Space. Base on this result, we also get some new and interesting results. The results in this paper generalize, extend, and unify some well-known strong convergence results in the literature.
C E Chidume - One of the best experts on this subject based on the ideXlab platform.
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a strong convergence theorem for generalized φ strongly monotone maps with applications
Fixed Point Theory and Applications, 2019Co-Authors: C E Chidume, Monday Ogudu Nnakwe, A AdamuAbstract:Let X be a uniformly convex and uniformly smooth Real Banach Space with dual Space $X^{*}$ . In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-strongly monotone map is constructed. A strong convergence theorem for a sequence generated by the algorithm is proved. Furthermore, the theorem is applied to approximate the solution of a convex optimization problem, a Hammerstein integral equation, and a variational inequality problem. This theorem generalizes, improves, and complements some recent results. Finally, examples of generalized-Φ-strongly monotone maps are constructed and numerical experiments which illustrate the convergence of the sequence generated by our algorithm are presented.
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convergence of the mann iteration algorithm for a class of pseudocontractive mappings
Applied Mathematics and Computation, 2007Co-Authors: C E Chidume, Mujahid AbbasAbstract:Let K be a nonempty, closed and convex subset of a Real Banach Space E. Let T:K->K be a strictly pseudocontractive map in the sense of Browder and Petryshyn. For a fixed x"[email protected]?K, define a sequence {x"n} byx"n"+"1=([email protected]"n)x"[email protected]"nTx"n,where {@a"n} is a Real sequence defined in [0,1] satisfying the following conditions (i) @?"n"="1^[email protected]"n=~, (ii) @?"n"="1^[email protected]"n^2 "[email protected]?x"n-Tx"[email protected]?=0. If, in addition, T is demicompact, then {x"n} converges strongly to some fixed point of T.
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approximate fixed point sequences and convergence theorems for lipschitz pseudocontractive maps
Proceedings of the American Mathematical Society, 2004Co-Authors: C E Chidume, Habtu ZegeyeAbstract:Let K be a nonempty closed convex subset of a Real Banach Space E and T be a Lipschitz pseudocontractive self-map of K with F(T) := {x E K : Tx = x} ¬= O. An iterative sequence {x n } is constructed for which ∥x n - Tx n ∥ → 0 as n → oc. If, in addition, K is assumed to be bounded, this conclusion still holds without the requirement that F(T) ¬= O. Moreover, if, in addition, E has a uniformly Gâteaux differentiable norm and is such that every closed bounded convex subset of K has the fixed point property for nonexpansive self-trappings, then the sequence {x n } converges strongly to a fixed point of T. Our iteration method is of independent interest.
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iterative solution of nonlinear equations with strongly accretive operators
Journal of Mathematical Analysis and Applications, 1995Co-Authors: C E ChidumeAbstract:Abstract Let E be a Real Banach Space with a uniformly convex dual. Suppose T : E → E is a strongly accretive map with bounded range such that for each ƒ ∈ E the equation Tx = ƒ has a solution in E . It is proved that each of the two well known fixed point iteration methods (the Mann and Ishikawa iteration methods), under suitable conditions, converges strongly to a solution of the equation Tx = ƒ. Furthermore, our method shows that such a solution is necessarily unique. Explicit error estimates are given. Our results resolve in the affirmative an open problem ( J. Math, Anal, Appl . 151, No. 2 (1990), 460) and generalize important known results.
Monday Ogudu Nnakwe - One of the best experts on this subject based on the ideXlab platform.
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A common solution of generalized equilibrium problems and fixed points of pseudo-contractive-type maps
Journal of Applied Mathematics and Computing, 2020Co-Authors: Monday Ogudu Nnakwe, Chibueze Christian OkekeAbstract:In this paper, a new iterative algorithm of a Halpern-type is constructed. The sequence generated by the algorithm is proved to converge strongly to a common solution of two generalized equilibrium problems and a common J -fixed point of two continuous J -pseudo-contractive maps in a uniformly smooth and uniformly convex Real Banach Space. Furthermore, a numerical example is given to illustrate the implementability of our algorithm. Finally, the theorem complements, improves and unifies some related recent results in the literature.
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a strong convergence theorem for generalized φ strongly monotone maps with applications
Fixed Point Theory and Applications, 2019Co-Authors: C E Chidume, Monday Ogudu Nnakwe, A AdamuAbstract:Let X be a uniformly convex and uniformly smooth Real Banach Space with dual Space $X^{*}$ . In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-strongly monotone map is constructed. A strong convergence theorem for a sequence generated by the algorithm is proved. Furthermore, the theorem is applied to approximate the solution of a convex optimization problem, a Hammerstein integral equation, and a variational inequality problem. This theorem generalizes, improves, and complements some recent results. Finally, examples of generalized-Φ-strongly monotone maps are constructed and numerical experiments which illustrate the convergence of the sequence generated by our algorithm are presented.
