Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces

By Wataru Takahashi, Y. Takeuchi, Rieko Kubota. 2008

365 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6acb1e377c2625ef2da0320c0cb3e21a4de5902a

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In Computational Theory and Mathematics

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In Numerical Analysis

Citations in the corpus

A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping (2009, background): “Our results are connected with Tada and Takahashi’s result [19] and Takahashi’s et al. result [ 23 ].”
Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings (2011, methodology): “[25] further improved Theorem TZ by considering shrinking projection methods which were introduced in [34] for quasi-j-nonexpansive mappings in a uniformly convex and uniformly smooth Banach space.”
Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces (2010, methodology): “The following algorithm is based on the concept of the so-called shrinking projection method which was introduced by Takahashi, Takeuchi and Kubota in [27].”
Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space (2011, methodology): “[26] presented an algorithm for finding a fixed point of a nonexpansive mapping S in Hilbert space.”
A projection method for solving nonlinear problems in reflexive Banach spaces (2011, methodology): “A Strong Convergence Theorem The following algorithm is based on the concept of the so-called shrinking projection method, which was introduced by Takahashi, Takeuchi and Kubota in [30].”
Parallel and sequential hybrid methods for a finite family of asymptotically quasi $$\phi $$ϕ-nonexpansive mappings (2015, background): “[29], Takahashi and Zembayashi [30], Wang and Xuan [32], Reich and Sabach [24,25], Kang et al.”
Outer approximation methods for solving variational inequalities in Hilbert space (2017, methodology): “One could, for example, assume a variant of (28), where instead of the trajectory of method (25), any arbitrary sequence is used, as in [30,49].”
The split common null point problem and the shrinking projection method in Banach spaces (2016, background): “[7], Takahashi [8] proved the following theorem; see also [9].”
The shrinking projection method for a finite family of demimetric mappings with variational inequality problems in a Hilbert space (2018, methodology): “On the other hand, we know the shrinking projection method which was introduced by Takahashi, Takeuchi and Kubota [17] for finding a fixed point of a nonexpansive mapping in a Hilbert space.”