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Numerical Algorithms - We consider the monotone variational inequality problem in a Hilbert space and describe a projection-type method with inertial terms under the following properties: (a) The... 相似文献
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ABSTRACTIn this paper, we investigate the problem of finding a common solution to a fixed point problem involving demi-contractive operator and a variational inequality with monotone and Lipschitz continuous mapping in real Hilbert spaces. Inspired by the projection and contraction method and the hybrid descent approximation method, a new and efficient iterative method for solving the problem is introduced. Strong convergence theorem of the proposed method is established under standard and mild conditions. Our scheme generalizes and extends some of the existing results in the literature, and moreover, its computational effort is less per each iteration compared with related works. 相似文献
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Our aim in this paper is to study strong convergence results for L-Lipschitz continuous monotone variational inequality but L is unknown using a combination of subgradient extra-gradient method and viscosity approximation method with adoption of Armijo-like step size rule in infinite dimensional real Hilbert spaces. Our results are obtained under mild conditions on the iterative parameters. We apply our result to nonlinear Hammerstein integral equations and finally provide some numerical experiments to illustrate our proposed algorithm. 相似文献
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The purpose of this paper is to study some iterative algorithms for finding a common element of the set of solutions of systems of variational inequalities for inverse-strongly accretive mappings and the set of fixed points of an asymptotically nonexpansive mapping in uniformly convex and 2-uniformly smooth Banach space or uniformly convex and q-uniformly smooth Banach space. Strong convergence theorems are obtained under suitable conditions. We also give some numerical examples to support our main results. The results obtained in this paper improve and extend the recent ones announced by many others in the literature. 相似文献
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Yekini Shehu 《Annali dell'Universita di Ferrara》2010,56(2):345-368
In this paper, we introduce a new iterative scheme for finding a common element of the set of fixed points of a nonexpansive
mapping, the set of solution of generalized equilibrium problem and the set of solutions of the variational inequality problem
for a co-coercive mapping in a real Hilbert space. Then strong convergence of the scheme to a common element of the three
sets is proved. Furthermore, new convergence results are deduced and finally we apply our results to solving optimization
problems and obtaining zeroes of maximal monotone operators and co-coercive mappings. 相似文献
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In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature. 相似文献
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Yekini Shehu 《Annali dell'Universita di Ferrara》2012,58(2):371-387
In this paper, we introduce a new iterative scheme by hybrid methods and prove strong convergence of the scheme for approximation of a common fixed point of two countably infinite families of multi valued nonexpansive mappings which is also a solution to system equilibrium problems and system of variational inequality problems in a real Hilbert space. Our results extend important recent results. 相似文献
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Yekini Shehu 《Optimization Letters》2012,6(7):1485-1497
In this paper, we construct a new iterative scheme by hybrid method for approximation of common element of set of zeroes of a finite family of ??-inverse-strongly monotone operators and set of common solutions to a system of generalized mixed equilibrium problems in a 2-uniformly convex real Banach space which is also uniformly smooth. Then, we prove strong convergence of the scheme to a common element of the two sets. 相似文献
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Gang Cai Aviv Gibali Olaniyi S. Iyiola Yekini Shehu 《Journal of Optimization Theory and Applications》2018,178(1):219-239
In this paper, we study the variational inequalities involving monotone and Lipschitz continuous mapping in Banach spaces. A new and simple iterative method, which combines Halpern’s technique and the subgradient extragradient idea, is given. Under mild and standard assumptions, we establish the strong convergence of our algorithm in a uniformly smooth and convex Banach spaces. We also present a modification of our method using a line-search approach, this enable to obtain strong convergence in real and reflexive Banach spaces, without the prior knowledge of the Lipschitz constant. Numerical experiments illustrate the performances of our new algorithm and provide a comparison with related algorithms. Our results generalize and extend some of the existing works in Hilbert spaces to Banach spaces as well as provide an extension from weak to strong convergence. 相似文献
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Yekini SHEHU 《数学物理学报(B辑英文版)》2014,(4):1081-1097
In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature. 相似文献