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Some fixed point theorems for set-valued mappings in uniform spaces

100%

Turkoglu D. , Ozer O. , Fisher B.

Demonstratio Mathematica

1999

tom Vol. 32, nr 2

394-400

Closedness of certain classes of functions in the topology of uniform convergence

100%

Kohli J. K. , Aggarwal J.

Demonstratio Mathematica

2012

tom Vol. 45, nr 4

947-952

In this paper, closedness of certain classes of functions in VX in the topology of uniform convergence is observed. In particular, we show that the function spaces SC(X, Y) of quasi continuous (…) functions, (…) (X, Y ) of (…)-continuous functions and L(X,Y) of cl-supercontinuous functions are closed in YX in the topology of uniform convergence.

Some common fixed point theorems for selfmappings satisfying two contractive conditions of integral type in a uniform space

100%

Olatinwo M.

Open Mathematics

2008

tom 6

nr 2

335-341

In this paper, we establish some common fixed point theorems for selfmappings of a uniform space by employing both the concepts of an A-distance and an E-distance introduced by Aamri and El Moutawakil [1] and two contractive conditions of integral type. Our results are generalizations and extensions of the classical Banach’s fixed point theorem of [2, 3, 19], some results of Aamri and El Moutawakil [1], Theorem 2.1 of Branciari [5] as well as a result of Jungck [7].

On cliquishness of maps of two variables

88%

Ewart J.

Demonstratio Mathematica

2002

tom Vol. 35, nr 3

657-670

We give some sufficient conditions under which a separately cliquish map of two variables is cliquish.

Uniform Space

75%

Coghetto R.

Formalized Mathematics

2016

tom 24

nr 3

215-226

In this article, we formalize in Mizar [1] the notion of uniform space introduced by André Weil using the concepts of entourages [2]. We present some results between uniform space and pseudo metric space. We introduce the concepts of left-uniformity and right-uniformity of a topological group. Next, we define the concept of the partition topology. Following the Vlach’s works [11, 10], we define the semi-uniform space induced by a tolerance and the uniform space induced by an equivalence relation. Finally, using mostly Gehrke, Grigorieff and Pin [4] works, a Pervin uniform space defined from the sets of the form ((X\A) × (X\A)) ∪ (A×A) is presented.

Compact and bounded sets in intuitionistic fuzzy metric spaces

75%

Efe H. , Alaca C.

Demonstratio Mathematica

2007

tom Vol. 40, nr 2

449-456

The purpose of this paper is to define q-bounded, semi-bounded, totally bounded, and unbounded sets in an intuitionistic fuzzy metric space X and study the relation between F-bounded sets and the above mentioned sets and prove that the statements (a) X is compact (b) X is sequentially compact and (c) X is complete and totally bounded are all equivalent in an intuitionistic fuzzy metric space X.

Remarks on a paper by Beg, latif and Minhas about fixed points

63%

Jachymski J.

Demonstratio Mathematica

1998

tom Vol. 31, nr 2

333-338

Asymptotic behavior of relatively nonexpansive operators in Banach spaces

51%

Butnariu D. , Reich S. , Zaslavski A. J.

Journal of Applied Analysis

2001

tom Vol. 7, nr 2

151-174

Let K be a closed convex subset of a Banach space X and let F be a nonempty closed convex subset of K. We consider complete metric spaces of self-mappings of K which fix all the points of F and are relatively nonexpansive with respect to a given convex function f on X. We prove (under certain assumptions on f) that the iterates of a generic mapping in these spaces converge strongly to a retraction onto F.

Remarks on some variants of minimal point theorem and Ekeland variational principle with applications

44%

Meghea I. , Stamin C. S.

Demonstratio Mathematica

2022

tom Vol. 55, nr 1

354--379

This paper presents some variants of minimal point theorem together with corresponding variants of Ekeland variational principle. In the second part of this article, there is a discussion on Ekeland variational principle and minimal point theorem relative to it in uniform spaces. The aim of these series of important results is to highlight relations between them, some improvements and specific applications.