Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings

By N. Nadezhkina, Wataru Takahashi. 2006

402 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2f5010d166147c19733fdf7565d96fd224224a67

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

STRONG CONVERGENCE THEOREM BY AN EXTRAGRADIENT METHOD FOR FIXED POINT PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS (2006, methodology): “Further motivated by the idea of Korpelevich’s extragradient method, Nadezhkina and Takahashi [10] introduced an iterative process for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem.”
Algorithms for the Split Variational Inequality Problem (2010, background): “Takahashi and Nadezhkina [35] proposed an algorithm for finding a point x∗ ∈ Fix(N)∩SOL(C, f ), where N : C → C is a nonexpansive operator.”
A hybrid extragradient method extended to fixed point problems and equilibrium problems (2013, methodology): “1 kxnþ1 xnk ¼ 0: As in Nadezhkina and Takahashi [16] when C¼H we give the following application of Theorem 3.3.”
Iterative algorithm with self-adaptive step size for approximating the common solution of variational inequality and fixed point problems (2021, methodology): “Takahashi and Toyoda [27] considered the problem of finding a common solution of VIP and f(p)P for a nonexpansive mapping and introduced the following algorithm to generate sequence {xn}. xn+1 = (1 − αn)xn + αnS′PC(xn − λnAxn), (8) whereA : C → H is an inverse strongly monotone operator, S′ : C → C ”
On extragradient-viscosity methods for solving equilibrium and fixed point problems in a Hilbert space (2015, background): “[7–14] The motivation for studying such a problem is in its possible application to mathematical models whose constraints can be expressed as fixed point problems and/or variational inequalities.”
Weak Convergence of an Iterative Method for Pseudomonotone Variational Inequalities and Fixed-Point Problems (2010, neutral): “, [8–13].”
Algorithms of common solutions to quasi variational inclusion and fixed point problems (2008, methodology): “The results presented in the paper not only improve and extend the main result in Korpelevich [15] , but also replenish and extend the corresponding results in Iiduka and Takahashi [13] , Takahashi and Toyoda [12] , Nadezhkina and Takahashi [ 14 ] and Zeng and Yao [16] .”
An Extragradient Method for Fixed Point Problems and Variational Inequality Problems (2007, methodology): “Theorem 1.1 (see Nadezhkina and Takahashi [8]).”
Weak Convergence Theorem by an Extragradient Method for Variational Inequality, Equilibrium and Fixed Point Problems (2009, methodology): “Then, we prove a weak convergence theorem, which is connected with Korpelevičs extragradient method [5] and Nadezhkina and Takahashi’s result [7].”