Viscosity approximations by the shrinking projection method in Hilbert spaces

AbstractWe consider viscosity approximations by using the shrinking projection method established by Takahashi, Takeuchi, and Kubota, and the modified shrinking projection method proposed by Qin, Cho, Kang, and Zhou, for finding a common fixed point of countably many nonlinear mappings, and we prove strong convergence theorems which extend some known results. We also consider semigroups of nonlinear mappings and obtain strong convergence of iterative schemes which approximate a common fixed point of the semigroup under certain conditions

The Problem of Image Recovery by the Metric Projections in Banach Spaces

We consider the problem of image recovery by the metric projections in a real Banach space. For a countable family of nonempty closed convex subsets, we generate an iterative sequence converging weakly to a point in the intersection of these subsets. Our convergence theorems extend the results proved by Bregman and Crombez

Some Characterizations for a Family of Nonexpansive Mappings and Convergence of a Generated Sequence to Their Common Fixed Point

Motivated by the method of Xu (2006) and Matsushita and Takahashi (2008), we characterize the set of all common fixed points of a family of nonexpansive mappings by the notion of Mosco convergence and prove strong convergence theorems for nonexpansive mappings and semigroups in a uniformly convex Banach space.</p

Some Characterizations for a Family of Nonexpansive Mappings and Convergence of a Generated Sequence to Their Common Fixed Point

Motivated by the method of Xu (2006) and Matsushita and Takahashi (2008), we characterize the set of all common fixed points of a family of nonexpansive mappings by the notion of Mosco convergence and prove strong convergence theorems for nonexpansive mappings and semigroups in a uniformly convex Banach space

Strong Convergence to a Solution of a Variational Inequality Problem in Banach Spaces

We consider the variational inequality problem for a family of operators of a nonempty closed convex subset of a 2-uniformly convex Banach space with a uniformly Gâteaux differentiable norm, into its dual space. We assume some properties for the operators and get strong convergence to a common solution to the variational inequality problem by the hybrid method proposed by Haugazeau. Using these results, we obtain several results for the variational inequality problem and the proximal point algorithm