Displaying similar documents to “Nonlinear ergodic theorems for asymptotically almost nonexpansive curves in a Hilbert space.”

The super fixed point property for asymptotically nonexpansive mappings

Andrzej Wiśnicki (2012)

Fundamenta Mathematicae

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We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive mappings in uniformly nonsquare and uniformly noncreasy Banach spaces. The results are generalized to commuting families of asymptotically nonexpansive mappings.

Nonexpansive retractions in Hilbert spaces

Kazimierz Goebel, Ewa Sędłak (2009)

Annales UMCS, Mathematica

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Let H be a Hilbert space and C ⊂ H be closed and convex. The mapping P: H → C known as the nearest point projection is nonexpansive (1-lipschitzian). We observed that, the natural question: "Are there nonexpansive projections Q: H → C other than P?" is neglected in the literature. Also, the answer is not often present in the "folklore" of the Hilbert space theory. We provide here the answer and discuss some facts connected with the subject.

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.