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It is proved that: for every Banach space $X$ which has uniformly normal structure there exists a $k > 1$ with the property: if $A$ is a nonempty bounded closed convex subset of $X$ and $T : A \to A$ is an asymptotically regular mapping such that $\underset{n \to \infty}{lim inf} | | | T^{n} | | | < k,$ where $| | | T | | |$ is the Lipschitz constant (norm) of $T$ , then $T$ has a fixed point in $A$ .

Fixed points of asymptotically regular nonexpansive mappings on nonconvex sets.

Kaczor, Wiesława (2003)

Abstract and Applied Analysis

Fixed points of condensing multivalued maps in topological vector spaces.

Kim, In-Sook (2004)

Fixed Point Theory and Applications [electronic only]

Fixed points of cone compression and expansion multimaps defined on Fréchet spaces: the projective limit approach.

Agarwal, Ravi P., O'Regan, Donal (2006)

Journal of Applied Mathematics and Stochastic Analysis

Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces

Daya Ram Sahu (2005)

Commentationes Mathematicae Universitatis Carolinae

We introduce the classes of nearly contraction mappings and nearly asymptotically nonexpansive mappings. The class of nearly contraction mappings includes the class of contraction mappings, but the class of nearly asymptotically nonexpansive mappings contains the class of asymptotically nonexpansive mappings and is contained in the class of mappings of asymptotically nonexpansive type. We study the existence of fixed points and the structure of fixed point sets of mappings of these classes in Banach...

Fixed points of discontinuous multivalued operators in ordered spaces with applications.

Hong, Shihuang, Qiu, Zheyong (2010)

Fixed Point Theory and Applications [electronic only]

Fixed points of holomorphic mappings for domains in Banach spaces.

Harris, Lawrence A. (2003)

Abstract and Applied Analysis

Fixed points of holomorphic mappings in the Hilbert ball

T. Kuczumow (1988)

Colloquium Mathematicae

Fixed points of Lipschitzian semigroups in Banach spaces

Jarosław Górnicki (1997)

Studia Mathematica

We prove the following theorem: Let p > 1 and let E be a real p-uniformly convex Banach space, and C a nonempty bounded closed convex subset of E. If $T = T_{s} : C \to C : s \in G = [0, \infty)$ is a Lipschitzian semigroup such that $g = l i m i n f_{G ∋ α \to \infty} i n f_{G ∋ δ \geq 0} 1 / α ʃ_{0}^{α} ∥ T_{β + δ} ∥^{p} d β < 1 + c$ , where c > 0 is some constant, then there exists x ∈ C such that $T_{s} x = x$ for all s ∈ G.

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