Amenability and Fixed Point Properties of Semitopological Semigroups in Modular Vector Spaces

2019 ◽  
Vol 63 (3) ◽  
pp. 692-704
Author(s):  
Khadime Salame
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nonexpansive Mappings ◽  
Continuous Functions ◽  
Modular Space ◽  
Modular Spaces ◽  
Fixed Point Properties ◽  
Uniformly Continuous ◽  
Locally Convex

AbstractIn this paper, we initiate the study of fixed point properties of amenable or reversible semitopological semigroups in modular spaces. Takahashi’s fixed point theorem for amenable semigroups of nonexpansive mappings, and T. Mitchell’s fixed point theorem for reversible semigroups of nonexpansive mappings in Banach spaces are extended to the setting of modular spaces. Among other things, we also generalize another classical result due to Mitchell characterizing the left amenability property of the space of left uniformly continuous functions on semitopological semigroups by introducing the notion of a semi-modular space as a generalization of the concept of a locally convex space.

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 More about metric spaces on which continuous functions are uniformly continuous

1986 ◽  
Vol 33 (3) ◽  
pp. 397-406 ◽  
Author(s):  
Gerald Beer
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Continuous Functions ◽  
Function Form ◽  
Uniformly Continuous

An Atsuji space is a metric space X such that each continuous function form X to an arbitrary metric space Y is uniformly continuous. We here present (i) characterizations of metric spaces with Atsuji completions; (ii) Cantor-type theorems for Atsuji spaces; (iii) a fixed point theorem for self-maps of an Atsuji space.

scholarly journals On Approximate Coincidence Point Properties and Their Applications to Fixed Point Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cone Metric Spaces ◽  
Fixed Point Properties ◽  
Contractive Maps

We first establish some existence results concerning approximate coincidence point properties and approximate fixed point properties for various types of nonlinear contractive maps in the setting of cone metric spaces and general metric spaces. From these results, we present some new coincidence point and fixed point theorems which generalize Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and some well-known results in the literature.

scholarly journals On some theorems of Tarafdar

1976 ◽  
Vol 15 (2) ◽  
pp. 213-221
Author(s):  
S.A. Husain ◽  
V.M. Sehgal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Vector Space ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Locally Convex ◽  
Common Fixed Point Theorem

In a recent paper (Bull. Austral. Math. Soc. 13 (1975), 241–245), Tarafdar has considered nonexpansive self mappings on a subset X of a locally convex vector space E and proved an extension to E of a theorem of Göhde. The purpose of this paper is to show that the condition f: X → X, in Göhde-Tarafdar's Theorem in the above paper, may be weakened to f: X → E with f(∂X) ⊆ X. As a consequence, it is further shown that an extension to E of a well-known common fixed point theorem of Belluce and Kirk due to Tarafdar remains true on domains that are not necessarily bounded or quasi-complete.

scholarly journals Two Fixed-Point Theorems for Mappings Satisfying a General Contractive Condition of Integral Type in the Modular Space

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Maryam Beygmohammadi ◽  
Abdolrahman Razani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Modular Space ◽  
Contractive Condition ◽  
Integral Type

First we prove existence of a fixed point for mappings defined on a complete modular space satisfying a general contractive inequality of integral type. Then we generalize fixed-point theorem for a quasicontraction mapping given by Khamsi (2008) and Ciric (1974).

scholarly journals An extension of a theorem of Sahab, Khan, and Sessa

2001 ◽  
Vol 27 (11) ◽  
pp. 701-706 ◽  
Author(s):  
A. R. Khan ◽  
N. Hussain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Locally Convex Spaces ◽  
Invariant Approximation ◽  
Recent Theorem ◽  
Locally Convex ◽  
Convex Spaces

A fixed point theorem of Fisher and Sessa is generalized to locally convex spaces and the new result is applied to extend a recent theorem on invariant approximation of Sahab, Khan, and Sessa.

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.

scholarly journals Fixed point approximation of Presic nonexpansive mappings in product of CAT (0) spaces

2016 ◽  
Vol 32 (3) ◽  
pp. 315-322
Author(s):  
HAFIZ FUKHAR-UD-DIN ◽  
◽  
VASILE BERINDE ◽  
ABDUL RAHIM KHAN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Banach Spaces ◽  
Point Theorem ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Control Parameters ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces

We obtain a fixed point theorem for Presiˇ c nonexpansive mappings on the product of ´ CAT (0) spaces and approximate this fixed points through Ishikawa type iterative algorithms under relaxed conditions on the control parameters. Our results are new in the literature and are valid in uniformly convex Banach spaces.

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