Viscosity iterative algorithm for variational inequality problems and fixed point problems in a real q-uniformly smooth Banach space

被引：0
作者：
Gang Cai
机构：
[1] Chongqing Normal University,School of Mathematics Science
来源：
Fixed Point Theory and Applications | / 2015卷
关键词：
strong convergence; variational inequality; fixed point; strict pseudocontraction; -uniformly smooth Banach space; 49J30; 47H10; 47H17; 49M05;
D O I：
暂无
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摘要：
The purpose of this paper is to study a viscosity iterative algorithm for finding a common element of the set of solutions of a general variational inequality problem for two inverse strongly accretive operators and the set of fixed points of a δ-strict pseudocontraction in a real q-uniformly smooth Banach space. Some strong convergence theorems are obtained under appropriate conditions. As an application, we prove some strong convergence theorems for fixed point problems and variational inequality problems or equilibrium problems in Hilbert spaces. These results improve and extend the corresponding results announced by many others.
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[1]  
Iiduka H(2004)Approximation of solutions of variational inequalities for monotone mappings Panam. Math. J. 14 49-61
[2]  
Takahashi W(2006)Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems Taiwan. J. Math. 10 1293-1303
[3]  
Toyoda M(2006)Weak convergence of an iterative sequence for accretive operators in Banach spaces Fixed Point Theory Appl. 2006 375-390
[4]  
Zeng LC(2008)Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities Math. Methods Oper. Res. 67 776-787
[5]  
Yao JC(2007)On viscosity iterative methods for variational inequalities J. Math. Anal. Appl. 325 217-229
[6]  
Aoyama K(2000)New approximation schemes for general variational inequalities J. Math. Anal. Appl. 251 231-240
[7]  
Iiduka H(2009)Convergence of an iterative algorithm for systems of variational in equalities and nonexpansive mappings with applications J. Comput. Appl. Math. 233 1211-1224
[8]  
Takahashi W(2010)Modified extragradient methods for a system of variational inequalities in Banach spaces Acta Appl. Math. 110 2567-2579
[9]  
Ceng LC(2011)Strong convergence theorems based on a new modified extragradient method for variational inequality problems and fixed point problems in Banach spaces Comput. Math. Appl. 62 635-646
[10]  
Wang C(2010)Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems J. Glob. Optim. 46 447-464
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