Journal ArticleDOI
Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings
Hideaki Iiduka,Wataru Takahashi +1 more
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In this article, an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space is introduced.Abstract:
In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common fixed point of a nonexpansive mapping and a strictly pseudocontractive mapping and the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping.read more
Citations
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Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space
TL;DR: In this article, a Halpern type iterative sequence is introduced to find a common fixed point of a family of nonexpansive mappings, and it is shown that such a sequence converges strongly to the common fixed points of a countable family of mappings.
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A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization
TL;DR: In this paper, a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem was introduced, and some strong convergence theorems for approximating the common elements of the above three sets are obtained.
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Convergence theorems of fixed points for κ-strict pseudo-contractions in Hilbert spaces
TL;DR: In this article, Marino et al. presented a strong convergence theorem for κ-strict pseudo-contractions in real Hilbert spaces, where the control parameter sequence { α n } is chosen so that κ ≤ α n ≤ 1 and ∑ n = 1 ∞ ( α n − κ ) ( 1 − α n ) = ∞, then { x n } converges weakly to a fixed point of T.
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Algorithms of common solutions to quasi variational inclusion and fixed point problems
TL;DR: In this article, the authors present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued maximal monotone mapping and inverse-strongly-monotone mappings in Hilbert space.
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Strong convergence of a general iterative algorithm for equilibrium problems and variational inequality problems
TL;DR: The purpose of this paper is to study the strong convergence of a general iterative scheme to find a common element of the set of common fixed points of a finite family of nonexpansive mappings, theSet of solutions of variation inequalities for a relaxed cocoercive mapping and the setof solutions of an equilibrium problem.
References
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Journal ArticleDOI
Monotone Operators and the Proximal Point Algorithm
TL;DR: In this paper, the proximal point algorithm in exact form is investigated in a more general form where the requirement for exact minimization at each iteration is weakened, and the subdifferential $\partial f$ is replaced by an arbitrary maximal monotone operator T.
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Weak convergence of the sequence of successive approximations for nonexpansive mappings
Journal ArticleDOI
Construction of fixed points of nonlinear mappings in Hilbert space
F.E Browder,W. V. Petryshyn +1 more
TL;DR: In this paper, the existence of fixed points of non-compact mappings of a subset C of a Hilbert space H of a function space into H has been studied under a number of topological arguments.