scholarly journals Generalized trend constants of Lipschitz mappings

2018 ◽  
Vol 72 (2) ◽  
pp. 71
Author(s):  
Mariusz Szczepanik
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
Lipschitz Mappings ◽  
Trend Coefficient

In 2015, Goebel and Bolibok defined the initial trend coefficient of a mapping and the class of initially nonexpansive mappings. They proved that the fixed point property for nonexpansive mappings implies the fixed point property for initially nonexpansive mappings. We generalize the above concepts and prove an analogous fixed point theorem. We also study the initial trend coefficient more deeply.

scholarly journals General Higher-Order Lipschitz Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Joseph Frank Gordon
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonexpansive Mappings ◽  
Higher Order ◽  
Fixed Point Property ◽  
Point Property ◽  
New Class ◽  
Lipschitz Mappings ◽  
Approximate Fixed Point Property

In this paper, we introduce a new class of mappings and investigate their fixed point property. In the first direction, we prove a fixed point theorem for general higher-order contraction mappings in a given metric space and finally prove an approximate fixed point property for general higher-order nonexpansive mappings in a Banach space.

A note on Banach fixed point property

2021 ◽  
Vol 1 (1) ◽  
pp. 47-52
Author(s):  
Vlasta Matijević
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Closed Subspace ◽  
Short Note ◽  
Fixed Point Property ◽  
Banach Fixed Point Theorem ◽  
Point Property

In this short note we consider a sort of converse of the Banach fixed point theorem and prove that a metric space X is complete if and only if, for each closed subspace Y ⊆ X, any contraction f : Y → Y has a fixed point y ∈ Y.

scholarly journals A Fixed Point Theorem and the Existence of a Haar Measure for Hypergroups Satisfying Conditions Related to Amenability

2015 ◽  
Vol 58 (2) ◽  
pp. 415-422 ◽  
Author(s):  
Benjamin Willson
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Haar Measure ◽  
Continuous Functions ◽  
Fixed Point Property ◽  
Invariant Mean ◽  
Point Property ◽  
Uniformly Continuous

AbstractIn this paperwe present a fixed point property for amenable hypergroups that is analogous to Rickert’s fixed point theorem for semigroups. It equates the existence of a left invariant mean on the space of weakly right uniformly continuous functions to the existence of a fixed point for any action of the hypergroup. Using this fixed point property, certain hypergroups are shown to have a left Haar measure.

scholarly journals New Results and Generalizations for Approximate Fixed Point Property and Their Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Wei-Shih Du ◽  
Farshid Khojasteh
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Fixed Point Property ◽  
Point Property ◽  
Approximate Fixed Point ◽  
Nadler’S Fixed Point Theorem ◽  
Approximate Fixed Point Property

We first introduce the concept of manageable functions and then prove some new existence theorems related to approximate fixed point property for manageable functions andα-admissible multivalued maps. As applications of our results, some new fixed point theorems which generalize and improve Du's fixed point theorem, Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and Nadler's fixed point theorem and some well-known results in the literature are given.

A Fixed-Point Theorem for Commuting Monotone Functions

1969 ◽  
Vol 21 ◽  
pp. 502-504 ◽  
Author(s):  
William J. Gray
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Property ◽  
Point Property ◽  
Monotone Functions ◽  
Abelian Semigroup

Hamilton (1) proved that a hereditarily unicoherent, hereditarily decomposable metric continuum has the fixed-point property for homeomorphisms. In this paper we shall generalize this result by showing that if X is a hereditarily unicoherent, hereditarily decomposable Hausdorff continuum and 5 is an abelian semigroup of continuous monotone functions from X into X, then S leaves a point of X fixed.Let X be a Hausdorff continuum. X is unicoherent if, whenever X = A ∪ B, where A and B are subcontinua of X, A ∩ B is a continuum. If each subcontinuum of X is unicoherent, X is hereditarily unicoherent. X is decomposable if X is the union of two of its proper subcontinua. If each subcontinuum of X which contains more than one point is decomposable, X is hereditarily decomposable.

scholarly journals Towards the fixed point property for superreflexive spaces

2001 ◽  
Vol 64 (3) ◽  
pp. 435-444 ◽  
Author(s):  
Andrzej Wiśnicki
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Unit Sphere ◽  
Convex Set ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
Geometrical Condition

A Banach space X is said to have property (Sm) if every metrically convex set A ⊂ X which lies on the unit sphere and has diameter not greater than one can be (weakly) separated from zero by a functional. We show that this geometrical condition is closely connected with the fixed point property for nonexpansive mappings in superreflexive spaces.

scholarly journals Remarks on the stability of the fixed point property for nonexpansive mappings

2012 ◽  
Vol 1 (4) ◽  
pp. 417-430 ◽  
Author(s):  
Krzysztof Bolibok ◽  
Kazimierz Goebel ◽  
W. A. Kirk
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
The Stability

The fixed point property for some uniformly nonoctahedral Banach spaces

1999 ◽  
Vol 59 (3) ◽  
pp. 361-367 ◽  
Author(s):  
A. Jiménez-Melado
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Banach Spaces ◽  
Unit Sphere ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property

Roughly speaking, we show that a Banach space X has the fixed point property for nonexpansive mappings whenever X has the WORTH property and the unit sphere of X does not contain a triangle with sides of length larger than 2.

scholarly journals ORBITALLY NONEXPANSIVE MAPPINGS

2015 ◽  
Vol 93 (3) ◽  
pp. 497-503 ◽  
Author(s):  
ENRIQUE LLORENS-FUSTER
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nonexpansive Mappings ◽  
New Class ◽  
Nonlinear Mappings

We define a class of nonlinear mappings which is properly larger than the class of nonexpansive mappings. We also give a fixed point theorem for this new class of mappings.

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