Displaying similar documents to “A weak ergodic theorem for infinite products of Lipschitzian mappings.”

Two generic results in fixed point theory

Simeon Reich, Alexander J. Zaslavski (2007)

Banach Center Publications

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We give two examples of the generic approach to fixed point theory. The first example is concerned with the asymptotic behavior of infinite products of nonexpansive mappings in Banach spaces and the second with the existence and stability of fixed points of continuous mappings in finite-dimensional Euclidean spaces.

A common fixed point theorem for a commuting family of weak* continuous nonexpansive mappings

Sławomir Borzdyński, Andrzej Wiśnicki (2014)

Studia Mathematica

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It is shown that if 𝓢 is a commuting family of weak* continuous nonexpansive mappings acting on a weak* compact convex subset C of the dual Banach space E, then the set of common fixed points of 𝓢 is a nonempty nonexpansive retract of C. This partially solves an open problem in metric fixed point theory in the case of commutative semigroups.

On the fixed points of nonexpansive mappings in direct sums of Banach spaces

Andrzej Wiśnicki (2011)

Studia Mathematica

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We show that if a Banach space X has the weak fixed point property for nonexpansive mappings and Y has the generalized Gossez-Lami Dozo property or is uniformly convex in every direction, then the direct sum X ⊕ Y with a strictly monotone norm has the weak fixed point property. The result is new even if Y is finite-dimensional.

Convergence theorems for a finite family of nonexpansive and asymptotically nonexpansive mappings

Kittipong Sitthikul, Satit Saejung (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper, weak and strong convergence of finite step iteration sequences to a common fixed point for a pair of a finite family of nonexpansive mappings and a finite family of asymptotically nonexpansive mappings in a nonempty closed convex subset of uniformly convex Banach spaces are presented.

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

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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...