Theorem For Metric Spaces Research Articles

Minimization theorems for fixed point theorems in fuzzy metric spaces and applications

In this paper, we establish a minimization theorem in fuzzy metric spaces and make use of the result to obtain a fixed point theorem in fuzzy metric spaces which is similar to the Downing-Kirk fixed point theorem in metric spaces. As the consequences, we obtain Caristi's fixed point theorem and Ekeland's variational principle in fuzzy metric spaces and also give a direct simple proof of the equivalence between these two theorems. Some applications of these results to probabilistic metric spaces are presented.

A short proof of the Tietze-Urysohn extension theorem

Tietze [8] proved the extension theorem for metric spaces, and Urysohn I10] for normal topological spaces. Urysohn first proves his Lemma, which is a special case of the theorem. The proof of the lemma uses a set-theoretic argument which constructs a family of sets indexed by the rationals, and defines a continuous real-valued function using infima of subsets of the indices. In rather surprising contrast, the full extension theorem then makes use of infinite series, the Weierstrass M-test, and uniform convergence. The purpose of this note is to extend the method of Urysohn's Lemma so as to obtain the extension theorem directly, without the use of uniform convergence, and without first proving the lemma. Urysohn's Lemma itself is then no longer required, being an immediate corollary of the theorem.

A finiteness theorem for metric spaces

A finiteness theorem for metric spaces

On coincidence theorems for a family of mappings in convex metric spaces

In this paper, a theorem on common fixed points for a family of mappings defined on convex metric spaces is presented. This theorem is a generalization of the well known fixed point theorem proved by Assad and Kirk. As an application a common fixed point theorem in metric spaces with a convex structure is obtained.

A fixed point theorem for metric spaces

A fixed point theorem for metric spaces

Construction of homogeneous spaces of local functions and inverse approximation theorems

The paper's first part is devoted to the construction of systems, finitary inR n, of functions for approximations of the form The concepts of ℓ-approximating and-interpolating systems of functions are introduced, methods of constructing them are examined, and the labor consumption of the matrices of a variational-difference method is discussed when different systems of functions are used. The paper's second part contains inverse approximation theorems for metric spaces and their application in the case of approximations by spaces of local functions in Sobolev norms.

Some fixed point theorems in metric spaces

Some fixed point theorems in metric spaces

Some Fixed and Common Fixed Point Theorems in Metric Spaces

Let (X, d) be a metric space and Ti(i=l, 2) be self mappings of X. The purpose of this paper is to investigate the fixed and common fixed points of Ti, when the pair Ti(i=l, 2) satisfies a condition of the following type:(1)

On a Fixed-Point Theorem for Metric Spaces

On a Fixed-Point Theorem for Metric Spaces

On a Theorem in Metric Spaces

On a Theorem in Metric Spaces

A mapping theorem for metric spaces

A mapping theorem for metric spaces