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Convergence theorems by hybrid projection methods for Lipschitz-continuous monotone mappings and a countable family of nonexpansive mappings

Somyot Plubtieng; Poom Kumam — 2011

Banach Center Publications

In this paper, we introduce two iterative schemes for finding a common element of the set of a common fixed points of a countable family of nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a Hilbert space by using the hybrid projection methods in the mathematical programming. Then we prove strong convergence theorems by the hybrid projection methods for a monotone, Lipschitz-continuous mapping and a countable family...

The characteristic of noncompact convexity and random fixed point theorem for set-valued operators

Poom Kumam; Somyot Plubtieng — 2007

Czechoslovak Mathematical Journal

Let $(Ω, Σ)$ be a measurable space, $X$ a Banach space whose characteristic of noncompact convexity is less than 1, $C$ a bounded closed convex subset of $X$ , $K C (C)$ the family of all compact convex subsets of $C .$ We prove that a set-valued nonexpansive mapping $T C \to K C (C)$ has a fixed point. Furthermore, if $X$ is separable then we also prove that a set-valued nonexpansive operator $T Ω \times C \to K C (C)$ has a random fixed point.

Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces.

Plubtieng, Somyot; Wangkeeree, Rabian — 2005

International Journal of Mathematics and Mathematical Sciences

Implicit iteration process of nonexpansive non-self-mappings.

Plubtieng, Somyot; Punpaeng, Rattanaporn — 2005

International Journal of Mathematics and Mathematical Sciences

Strong and weak convergence of modified Mann iteration for new resolvents of maximal monotone operators in Banach spaces.

Plubtieng, Somyot; Sriprad, Wanna — 2009

Abstract and Applied Analysis

An extragradient method and proximal point algorithm for inverse strongly monotone operators and maximal monotone operators in Banach spaces.

Plubtieng, Somyot; Sriprad, Wanna — 2009

Fixed Point Theory and Applications [electronic only]

A viscosity approximation method for finding common solutions of variational inclusions, equilibrium problems, and fixed point problems in Hilbert spaces.

Plubtieng, Somyot; Sriprad, Wanna — 2009

Fixed Point Theory and Applications [electronic only]

Hybrid methods for equilibrium problems and fixed points problems of a countable family of relatively nonexpansive mappings in Banach spaces.

Plubtieng, Somyot; Sriprad, Wanna — 2010

Fixed Point Theory and Applications [electronic only]

Hybrid iterative methods for convex feasibility problems and fixed point problems of relatively nonexpansive mappings in Banach spaces.

Plubtieng, Somyot; Ungchittrakool, Kasamsuk — 2008

Fixed Point Theory and Applications [electronic only]

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Currently displaying 1 – 17 of 17

Convergence theorems by hybrid projection methods for Lipschitz-continuous monotone mappings and a countable family of nonexpansive mappings

The characteristic of noncompact convexity and random fixed point theorem for set-valued operators

Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces.

Implicit iteration process of nonexpansive non-self-mappings.

Strong and weak convergence of modified Mann iteration for new resolvents of maximal monotone operators in Banach spaces.

An extragradient method and proximal point algorithm for inverse strongly monotone operators and maximal monotone operators in Banach spaces.

A viscosity approximation method for finding common solutions of variational inclusions, equilibrium problems, and fixed point problems in Hilbert spaces.

Hybrid methods for equilibrium problems and fixed points problems of a countable family of relatively nonexpansive mappings in Banach spaces.

Weak convergence theorems for a system of mixed equilibrium problems and nonspreading mappings in a Hilbert space.

Strong convergence theorem for equilibrium problems and fixed points of a nonspreading mapping in Hilbert spaces.

Iterative schemes for fixed points of relatively nonexpansive mappings and their applications.

Existence result of generalized vector quasiequilibrium problems in locally $G$ -convex spaces.

Hybrid iterative methods for convex feasibility problems and fixed point problems of relatively nonexpansive mappings in Banach spaces.

Existence results for system of variational inequality problems with semimonotone operators.

On the existence result for system of generalized strong vector quasiequilibrium problems.

Random three-step iteration scheme and common random fixed point of three operators.

Approximation of a common random fixed point for a finite family of random operators.