[PDF] Top 20 On relaxed and contraction proximal point algorithms in hilbert spaces
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On relaxed and contraction proximal point algorithms in hilbert spaces
... On the other hand, since the PPA does not necessarily converge strongly (see [5]), many authors have conducted worthwhile studies on modifying the PPA so that the strong convergence is guaranteed (see, for instance, ... See full document
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A General Projection Method for a System of Relaxed Cocoercive Variational Inequalities in Hilbert Spaces
... nonlinear relaxed cocoercive variational inequalities with three different relaxed cocoercive mappings and three quasi-nonexpansive mappings in the framework of Hilbert ...nonlinear relaxed ... See full document
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Relaxed alternating CQ algorithms for the split equality problem in Hilbert spaces
... in Hilbert spaces. By converting it to a coupled fixed-point equation, we propose a new algorithm for solving the ...new relaxed alternating algorithms for the SEP. The first ... See full document
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Convergence of algorithms for an infinite family nonexpansive mappings and relaxed cocoercive mappings in Hilbert spaces
... Let H be a real Hilbert space, whose inner product and norm are denoted by h·, ·i and k · k, respectively. Let C be a closed convex subset of H and let A : C → H be a nonlinear map. Let P C be the projection of H ... See full document
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On Over Relaxed Proximal Point Algorithms for Generalized Nonlinear Operator Equation with (A,η,m) Monotonicity Framework
... over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and ... See full document
6
Strong convergence of a relaxed CQ algorithm for the split feasibility problem
... infinite-dimensional Hilbert spaces. In this paper, we introduce a new relaxed CQ algorithm such that the strong convergence is guaranteed in infinite-dimensional Hilbert ... See full document
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Hybrid Approximate Proximal Point Algorithms for Variational Inequalities in Banach Spaces
... Let E be a real Banach space with the dual E ∗ . As usually, ·, · denotes the duality pairing between E and E ∗ . In particular, if E is a real Hilbert space, then ·, · denotes its inner product. Let C be a ... See full document
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Hybrid projected subgradient-proximal algorithms for solving split equilibrium problems and split common fixed point problems of nonexpansive mappings in Hilbert spaces
... convergent algorithms which combines diagonal subgradient method, projection method and proximal method to solve split equilibrium problems and split common fixed point problems of nonexpansive ... See full document
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Proximal point algorithms involving fixed points of nonexpansive mappings in \(\operatorname{CAT}(0)\) spaces
... We denote argmin y∈X f (y) by the set of minimizers of f . A successful and powerful tool for solving this problem is the well-known proximal point algorithm (shortly, the PPA) which was initiated by ... See full document
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The modified proximal point algorithm in Hadamard spaces
... with algorithms for solving a variety of problems which may appear in sciences and ...the proximal point algorithm (PPA), which was introduced by Martinet [1] and Rockafellar [2] in Hilbert ... See full document
10
Best proximity point theorems for Fρ-proximal contraction in modular function spaces
... proximity point results are the ones that provide sufficient conditions for the existence of a best proximity point and algorithms for finding best proximity points (see Definition ...proximity ... See full document
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Approximate Proximal Point Algorithms for Finding Zeroes of Maximal Monotone Operators in Hilbert Spaces
... From Theorem 2.7 and the same proof of Corollary 2.3, we have the following corollary. Corollary 2.8. Let H be a real Hilbert space, Ω a nonempty closed convex subset of H, and U : Ω → Ω a continuous and ... See full document
10
Super-Relaxed ()-Proximal Point Algorithms, Relaxed ()-Proximal Point Algorithms, Linear Convergence Analysis, and Nonlinear Variational Inclusions
... of proximal point algorithms with their applications to general nonlinear variational inclusion problems, and then we recall some significant developments, especially the relaxation of ... See full document
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Iterative Approaches to Find Zeros of Maximal Monotone Operators by Hybrid Approximate Proximal Point Methods
... inexact proximal point method ...approximate proximal point algorithms in Hilbert spaces; that is, they established strong and weak convergence theorems for modified ... See full document
18
Strong and Weak Convergence of the Modified Proximal Point Algorithms in Hilbert Space
... Let T be a monotone operator on a Hilbert space H. Then J r T is a single-valued nonexpansive mapping from RI rT to DI rT DT ∩ DI DT . When K is a nonempty closed convex subset of H such that DT ⊂ K ⊂ RI rT for ... See full document
11
Regularization Inertial Proximal Point Algorithm for Monotone Hemicontinuous Mapping and Inverse Strongly Monotone Mappings in Hilbert Spaces
... inertial proximal point algorithm, called regularization inertial proximal point algorithm, we obtain the strong convergence of the algorithm, and the strong convergence is proved for the ... See full document
10
Generalized contraction principle
... Fixed point theorems are proved for contraction maps on M-convex spaces... Fixed Point Theorems, Contraion principle, M-convex spaces..[r] ... See full document
6
On some Mann’s type iterative algorithms
... In order to ensure strong convergence, in the past years, the method has been modified in several directions: by Ishikawa [] using a double convex-combination, by Halpern [] using an anchor, by Moudafi [] using a ... See full document
16
The contraction-proximal point algorithm with square-summable errors
... by Xu [] and Kamimura-Takahashi [], is known as the contraction-proximal point algo- rithm (CPPA) [], which is indeed a combination of Halpern’s iteration and the PPA. There are various conditions ... See full document
10
Self Adaptive Algorithms for the Split Common Fixed Point Problem of the Demimetric Mappings
... fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear operator belongs to another fixed-point ...iterative ... See full document
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