In this paper, a regularization projection algorithm is investigated for solving common elements of an equilibrium problem, a variational inequality problem and a fixed point problem of a strictly pseudocontractive mapping. Strong convergence theorems are established in the framework of real Hilbert spaces.
Let X be a Banach space or a complete hyperbolic metric space. Let C be a nonempty, bounded, closed, and convex subset of X and T : C → C be a monotone nonexpansive mapping. In this paper, we show that if X is a Banach space which is uniformly convex in every direction or a uniformly convex hyperbolic metric space, then T has a fixed point. This is the analog to Browder and Göhde's fixed point theorem for monotone nonexpansive mappings.MSC: Primary 46B20; 45D05; secondary 47E10; 34A12
Let L ρ be a uniformly convex modular function space with a strong Opial property.Let T : C → C be an asymptotic pointwise nonexpansive mapping, where C is a ρ-a.e. compact convex subset of L ρ . In this paper, we prove that the generalized Mann and Ishikawa processes converge almost everywhere to a fixed point of T. In addition, we prove that if C is compact in the strong sense, then both processes converge strongly to a fixed point. MSC: Primary 47H09; Secondary 47H10
Let (X, · ) be a Banach space. Let C be a nonempty, bounded, closed, and convex subset of X and T : C → C be a monotone nonexpansive mapping. In this paper, it is shown that a technique of Mann which is defined byis fruitful in finding a fixed point of monotone nonexpansive mappings.MSC: Primary 06F30; 46B20; 47E10
Let X be a uniformly convex and 2-uniformly smooth Banach space. In this paper, we propose an implicit iterative method and an explicit iterative method for solving a general system of variational inequalities (in short, GSVI) in X based on Korpelevich's extragradient method and viscosity approximation method. We show that the proposed algorithms converge strongly to some solutions of the GSVI under consideration. When X is a 2-uniformly smooth Banach space with weakly sequentially continuous duality mapping, we also propose two methods, which were inspired and motivated by Korpelevich's extragradient method and Mann's iterative method. Furthermore, it is also proven that the proposed algorithms converge strongly to some solutions of the considered GSVI. MSC: 49J30; 47H09; 47J20
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.