Convergence theorems for common solutions of various problems with nonlinear mapping
TL;DR: In this paper, Qin et al. introduced a hybrid projection iterative scheme that converges strongly to a common element of the solution set of a generalized mixed equilibrium problem, the set of common fixed points for a family of hemi-relatively nonexpansive mappings in a Banach space.
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Abstract: In this paper, motivated and inspired by Zegeye and Shahzad (Nonlinear Anal. 70:2707-2716, 2009), Qin et al. (J. Comput. Appl. Math. 225(1):20-30, 2009) and Kimura and Takahashi (J. Math. Anal. Appl. 357:356-363, 2009), we introduce a new hybrid projection iterative scheme that converges strongly to a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of common fixed points for a family of hemi-relatively nonexpansive mappings in a Banach space.
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Citations
A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces
TL;DR: In this article, a regularization projection algorithm is investigated for solving common elements of an equilibrium problem, a variational inequality problem and a fixed point problem of a strictly pseudocontractive mapping.
System of Extended General Variational Inequalities for Relaxed Cocoercive Mappings in Hilbert Space
Kyung Soo Kim
- 11 Oct 2018
TL;DR: In this article, a system of extended general variational inequalities (SEGVI) with several nonlinear operators, more precisely, six relaxed (α, r ) -cocoercive mappings, is studied.
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Hybrid methods for common solutions in Hilbert spaces with applications
TL;DR: In this article, hybrid methods are investigated for treating common solutions of nonlinear problems and a strong convergence theorem is established in the framework of real Hilbert spaces, where the hybrid method is applied to the problem of solving a nonlinear problem.
Strong convergence theorems for solutions of fixed point and variational inequality problems
Lanxiang Yu,Jian-Min Song +1 more
TL;DR: In this article, the authors investigated viscosity approximation methods for finding a common element in the set of fixed points of a strict pseudocontraction and in the sets of solutions of a generalized variational inequality in the framework of Banach spaces.
Convergence of a regularization algorithm for nonexpansive and monotone operators in Hilbert spaces
Qing Yuan,Yunpeng Zhang +1 more
TL;DR: In this article, a regularization algorithm was proposed to solve the variational inequality, fixed point and generalized equilibrium problems in the framework of Hilbert spaces. And it was proved that the sequence generated in the regularization method converges strongly to a common solution of the three problems.
References
Weak Convergence of Orbits of Nonlinear Operators in Reflexive Banach Spaces
TL;DR: In this paper, the authors consider self-mappings of a closed convex subset of a reflexive Banach space and show that almost all of them share the property that they have a fixed point z T such that, for any x ∈ K, the orbit converges weakly to z T.
171
An iterative method for solving nonlinear equations
TL;DR: An iterative method for finding a solution of the equation f(x)=0 is presented in this article, which is based on some specially derived quadrature rules and it is shown that the method can give better results than the Newton method.
102
A new hybrid method for solving a generalized equilibrium problem, solving a variational inequality problem and obtaining common fixed points in Banach spaces, with applications☆
TL;DR: In this paper, a strong convergence theorem for finding a common element of the set of solutions for a generalized equilibrium problem, a variational inequality problem and a fixed point problem for maximal monotone mappings in a Banach space was proved.
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Strong convergence studied by a hybrid type method for monotone operators in a Banach space
Hideaki Iiduka,Wataru Takahashi +1 more
TL;DR: Theorem 3.3 as mentioned in this paper is a strong convergence theorem for finding a zero point of an inverse-strongly monotone operator in a Banach space, and the convergence theorem is also applied to the problem of finding a minimizer of a convex function.
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Convergence of a hybrid algorithm for a reversible semigroup of nonlinear operators in Banach spaces
TL;DR: In this paper, the authors studied hybrid iterative schemes of Halpern types for a semigroup ℑ = { T ( s ) : s ∈ S } of relatively nonexpansive mappings on a closed and convex subset C of a Banach space with respect to a sequence { μ n } of asymptotically left invariant means defined on an appropriate invariant subspace of l ∞ ( S ).
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