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

Meghea Irina, Stamin Cristina Stefania

Demonstratio Mathematica

2022

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.

Compact and bounded sets in intuitionistic fuzzy metric spaces

Efe H., Alaca C.

Demonstratio Mathematica

2007

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.

Hyperbolic equations in uniform spaces

Cholewa J. W., Dlotko T.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 3

249-263

The paper is devoted to the Cauchy problem for a semilinear damped wave equation in the whole of R^n. Under suitable assumptions a bounded dissipative semigroup of global solutions is constructed in a locally uniform space H[...]^R^n) x L[...](R^n). Asymptotic compactness of this semigroup and the existence of a global attractor are then shown.