Strong convergence of an iterative algorithm for variational inequalities in Banach spaces

In this paper, we construct a new simple algorithm for solving some variational inequality in Banach spaces. Furthermore, we prove that the proposed algorithm has strong convergence.

[1]  Wataru Takahashi,et al.  Weak and Strong Convergence of Solutions to Accretive Operator Inclusions and Applications , 2000 .

[2]  Muhammad Aslam Noor,et al.  Some developments in general variational inequalities , 2004, Appl. Math. Comput..

[3]  Alfredo N. Iusem,et al.  An interior point method with Bregman functions for the variational inequality problem with paramonotone operators , 1998, Math. Program..

[4]  Wataru Takahashi,et al.  Weak convergence of an iterative sequence for accretive operators in Banach spaces , 2006 .

[5]  Tomonari Suzuki,et al.  Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces , 2005 .

[6]  D. Lamberton,et al.  Variational inequalities and the pricing of American options , 1990 .

[7]  E. Zeidler Nonlinear functional analysis and its applications , 1988 .

[8]  Wataru Takahashi,et al.  APPROXIMATION OF SOLUTIONS OF VARIATIONAL INEQUALITIES FOR MONOTONE MAPPINGS , 2004 .

[9]  I. Yamada The Hybrid Steepest Descent Method for the Variational Inequality Problem over the Intersection of Fixed Point Sets of Nonexpansive Mappings , 2001 .

[10]  Jen-Chih Yao,et al.  Variational Inequalities with Generalized Monotone Operators , 1994, Math. Oper. Res..

[11]  E. G. Gol'shtein,et al.  Modified Lagrangians in Convex Programming and their Generalizations , 1979 .

[12]  Hong-Kun Xu Inequalities in Banach spaces with applications , 1991 .

[13]  Hong-Kun Xu,et al.  Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities , 2003 .

[14]  F. Browder Nonlinear functional analysis , 1970 .

[15]  F. Browder Nonlinear operators and nonlinear equations of evolution in Banach spaces , 1976 .

[16]  Wataru Takahashi,et al.  Image recovery by convex combinations of sunny nonexpansive retractions , 1993 .

[17]  Dong Yun-da,et al.  A NOTE ON AN ITERATIVE ALGORITHM FOR THE VARIATIONAL INEQUALITY PROBLEM , 2003 .

[18]  R. Glowinski Lectures on Numerical Methods for Non-Linear Variational Problems , 1981 .

[19]  Ronald E. Bruck Nonexpansive retracts of Banach spaces , 1970 .

[20]  Wataru Takahashi,et al.  Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings , 2003 .

[21]  Hong-Kun Xu Iterative Algorithms for Nonlinear Operators , 2002 .