APPROXIMATION OF SOLUTIONS OF VARIATIONAL INEQUALITIES FOR MONOTONE MAPPINGS

By Hideaki Iiduka, Wataru Takahashi, M. Toyoda. 2004

164 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/833e01ba509d0524f2fefbb19be771d3fe3cc6b4

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Citations in the corpus

Weak convergence of an iterative sequence for accretive operators in Banach spaces (2006, background): “[11] proved the following weak convergence theorem.”
Modified Extragradient Methods for a System of Variational Inequalities in Banach Spaces (2010, methodology): “Several numerical methods have been developed for solving variational inequalities and related optimization problems, see [1–45] and the references therein.”
Extensions of Korpelevich's extragradient method for the variational inequality problem in Euclidean space (2012, methodology): “[5] introduced an iterative method for solving the VIP(S, f ) in Hilbert space, but again they have to calculate the projection onto S twice.”
Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings (2005, unknown): “If A = I − T, where T is a nonexpansive mapping of C into itself and I is the identity mapping of H, then A is 1/2-inverse-strongly-monotone and V I(C,A) = F(T); see [3].”
Weak convergence of a projection algorithm for variational inequalities in a Banach space (2008, background): “An operator A of C into E∗ is said to be inverse-strongly-monotone [7,10,15] if there exists a positive real number α such that 〈x − y,Ax −Ay〉 α‖Ax −Ay‖2 for all x, y ∈ C.”
Weak Convergence of an Iterative Method for Pseudomonotone Variational Inequalities and Fixed-Point Problems (2010, unknown): “, [8–13].”
A general iterative method for approximation of fixed points and their applications (2013, unknown): “(see, [11, 12, 15, 16, 17, 18, 19, 21, 22, 24]).”
Strong convergence theorem for a common point of solution of variational inequality and fixed point problem (2012, unknown): “In this connection, when E = H, a Hilbert space and A is γ − inverse strongly monotone, Iiduka, Takahashi and Toyoda [4] studied the following iterative scheme, the so called hybrid projection iteration method : x 0 ∈ C, chosen arbitrary , x n +1 = P C n ∩ Q n ( x 0 ) , n ≥ 1 , (5) where { α n } is…”
STRONG CONVERGENCE THEOREMS BY THE HYBRID METHOD FOR FAMILIES OF NONEXPANSIVE MAPPINGS IN HILBERT SPACES (2006, background): “Later, Nakajo and Takahashi [14], Kikkawa and Takahashi [11], Atsushiba and Takahashi [3], Iiduka, Takahashi and Toyoda [9] and Iiduka and Takahashi [10] studied strong convergence of {xn} generated by type (2).”