Abstract:
Fixed point (especially, the minimum norm fixed point) computation is an interestingtopic due to its practical applications in natural science. The purpose of thepaper is devoted to finding the common fixed points of an infinite family of nonexpansivemappings. We introduce an iterative algorithm and prove that suggested schemeconverges strongly to the common fixed points of an infinite family of nonexpansivemappings under some mild conditions. As a special case, we can find the minimumnorm common fixed point of an infinite family of nonexpansive mappings.

Abstract:
Let C be a closed convex subset of a uniformly smooth Banach space E, and T:C→E a nonexpansive nonself-mapping satisfying the weakly inwardness condition such that F(T)≠∅, and f:C→C a fixed contractive mapping. For t∈(0,1), the implicit iterative sequence {xt} is defined by xt=P(tf(xt)

Abstract:
We study the strong convergence of a hybrid steepest descent method with variable parameters for the general variational inequality (GVI) . Consequently, as an application, we obtain some results concerning the constrained generalized pseudoinverse. Our results extend and improve the result of Yao and Noor (2007) and many others.

Abstract:
We study the strong convergence of a hybrid steepest descent method with variable parameters for the general variational inequality (GVI) (F,g,C). Consequently, as an application, we obtain some results concerning the constrained generalized pseudoinverse. Our results extend and improve the result of Yao and Noor (2007) and many others.

Abstract:
Let be a closed convex subset of a real Banach space , is continuous pseudocontractive mapping, and is a fixed -Lipschitzian strongly pseudocontractive mapping. For any , let be the unique fixed point of . We prove that if has a fixed point and has uniformly Gateaux differentiable norm, such that every nonempty closed bounded convex subset of has the fixed point property for nonexpansive self-mappings, then converges to a fixed point of as approaches to 0. The results presented extend and improve the corresponding results of Morales and Jung (2000) and Hong-Kun Xu (2004).

Abstract:
We first introduce and analyze an algorithm of approximating solutions of maximal monotone operators in Hilbert spaces. Using this result, we consider the convex minimization problem of finding a minimizer of a proper lower-semicontinuous convex function and the variational problem of finding a solution of a variational inequality.

Abstract:
Motivated by T. Suzuki, we show strong convergence theorems of the CQ method for nonexpansive semigroups in Hilbert spaces by hybrid method in the mathematical programming. The results presented extend and improve the corresponding results of Kazuhide Nakajo and Wataru Takahashi (2003).

Abstract:
We use strongly pseudocontractions to regularize a class of accretive variational inequalities in Banach spaces, where the accretive operators are complements of pseudocontractions and the solutions are sought in the set of fixed points of another pseudocontraction. In this paper, we consider an implicit scheme that can be used to find a solution of a class of accretive variational inequalities. Our results improve and generalize some recent results of Yao et al. (Fixed Point Theory Appl, doi:10.1155/2011/180534, 2011) and Lu et al. (Nonlinear Anal, 71(3-4), 1032-1041, 2009). 2000 Mathematics subject classification 47H05; 47H09; 65J15

Abstract:
We first introduce and analyze an algorithm of approximating solutions of maximal monotone operators in Hilbert spaces. Using this result, we consider the convex minimization problem of finding a minimizer of a proper lower-semicontinuous convex function and the variational problem of finding a solution of a variational inequality.

Abstract:
Motivated by T. Suzuki, we show strong convergence theorems of the CQ method for nonexpansive semigroups in Hilbert spaces by hybrid method in the mathematical programming. The results presented extend and improve the corresponding results of Kazuhide Nakajo and Wataru Takahashi (2003).