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On the existence of ɛ-fixed points

Tiziana Cardinali (2014)

Open Mathematics

In this paper we prove some approximate fixed point theorems which extend, in a broad sense, analogous results obtained by Brânzei, Morgan, Scalzo and Tijs in 2003. By assuming also the weak demiclosedness property we state two fixed point theorems. Moreover, we study the existence of ɛ-Nash equilibria.

On the fixed point property in direct sums of Banach spaces with strictly monotone norms

Stanisław Prus, Andrzej Wiśnicki (2008)

Studia Mathematica

It is shown that if a Banach space X has the weak Banach-Saks property and the weak fixed point property for nonexpansive mappings and Y has the asymptotic (P) property (which is weaker than the condition WCS(Y) > 1), then X ⊕ Y endowed with a strictly monotone norm enjoys the weak fixed point property. The same conclusion is valid if X admits a 1-unconditional basis.

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

Andrzej Wiśnicki (2011)

Studia Mathematica

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.

On the generalizations of Siegel's fixed point theorem.

J. S. Jung, S. S. Chang, B. S. Lee, Y. J. Cho, S. M. Kang (2001)

Mathware and Soft Computing

In this paper, we establish a new version of Siegel's fixed point theorem in generating spaces of quasi-metric family. As consequences, we obtain general versions of the Downing-Kirk's fixed point and Caristi's fixed point theorem in the same spaces. Some applications of these results to fuzzy metric spaces and probabilistic metric spaces are presented.

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