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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 → K C ( C ) has a fixed point. Furthermore, if X is separable then we also prove that a set-valued nonexpansive operator T Ω × C → K C ( C ) has a random fixed point.

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