The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based” algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuz...

The theories of metric spaces and fuzzy are crucial topics in mathematics. 
 Compactness is one the most important fundamental properties that have been widely used Functional Analysis. In this paper, definition compact soft space introduced some its theorems investigated. Also, sequentially locally defined relationships between them studied. Moreover, each previous two concepts several ot...

in this paper, we give some new definitions of m-fuzzy metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete m-fuzzy metric spaces.

In this paper, we introduce a stationary M∞-fuzzy metric on the set C B(X), where M∞-fuzzy metric can be thought of as the degree of nearness between two fuzzy sets with respect to any positive real number and C B(X) is the class of fuzzy sets with nonempty bounded closed α-cut sets. Under the φ-contraction conditions, we give some common fixed point theorems for self-mappings in the space C B(X).

In this paper, we study the existence of coupled coincidence andcoupled common fixed points for single-valued and fuzzy mappingsunder a contractive condition in metric space. Presented theoremsextend and improve the main results of Abbas and$acute{C}$iri$acute{c}$ {itshape et al.} [M. Abbas, L.$acute{C}$iri$acute{c}$, {itshape et al.}, Coupled coincidenceand common fixed point theorems for hybr...

In this paper we introduce a new notion of generalized metric, called i-metric. This generalization is made by changing the valuation space of the distance function. The result is an interesting distance function for the set of fuzzy numbers of Interval Type with non negative fuzzy numbers as values. This example of i-metric generates a topology in a very natural way, based on open balls. We pr...

We extend the concept of fuzzy integral based on ⊕-decomposable measure from nonnegative fuzzy measurable function to extended real-valued fuzzy measurable function. Further investigations of fuzzy integrals based on pseudo-additive decomposable measure are carried out. Meanwhile, the space (S(μ),σ(·,·)) of all fuzzy measurable function will be proved to be a pseudo-metric space. Finally, as an...

*Correspondence: [email protected] 1School of Mathematics and Statistics, Tianshui Normal University, Tianshui, 741001, P.R. China 2School of Mathematics, Beijing Institute of Technology, Beijing, 100081, P.R. China Full list of author information is available at the end of the article Abstract In the present paper, an extension of the Edelstein contraction theorem for cyclic contrac...