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Probabilistic generalized metric spaces and nonlinear contractions

Mbarki A., Naciri R.

Demonstratio Mathematica

2016

Vol. 49, nr 4

437--452

We give a probabilistic generalization of the theory of generalized metric spaces [2]. Then, we prove a fixed point theorem for a self-mapping of a probabilistic generalized metric space, satisfying the very general nonlinear contraction condition without the assumption that the space is Hausdorff.

Necessary and sufficient conditions for common fixed point theorems in fuzzy metric space

O'Regan D., Abbas M.

Demonstratio Mathematica

2009

Vol. 42, nr 4

887-900

The aim of this paper is to provide a necessary and sufficient condition for the existence of a common fixed point of three maps f , g and T in a complete fuzzy metric space under a general contractive condition. A common fixed point theorem for a pair of weakly biased mappings, which is more general than weakly compatible mappings is also proved.

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.

Compatible maps and compatible maps of types (alpha) and (beta) in instutionstic fuzzy metric spaces

Turkoglu D., Alaca C., Yildiz C.

Demonstratio Mathematica

2006

Vol. 39, nr 3

671-684

In this paper, we first formulate the definition of compatible maps and compatible maps of types (alpha) and (beta) in intuitionistic fuzzy metric spaces and give some relations between the concepts of compatible maps and compatible maps of types (alpha) and (beta).