After Zadeh pioneering’s paper [15], where the Theory of Fuzzy Sets was introduced, hundreds of examples have been supplied where the nature of uncertainty in the behavior of a given system possesses fuzzy rather than stochastic nature. Non-stationary fuzzy systems described by fuzzy processes look as their natural extension into the time domina. From different viewpoints they were carefully st...

A notion of completeness and completion suitable for use in the absence of countable choice is developed. This encompasses the construction of the real numbers as well as the completion of an arbitrary metric space. The real numbers are characterized as a complete archimedean Heyting …eld, a terminal object in the category of archimedean Heyting …elds.

Remark. The non-archimedean topology: Recall that if K is a field with a val­ uation | |, then it also is a metric space with d(x, y) = |x − y|. The topology has a basis of open neighborhoods given by B(x, ǫ) = {y ∈ K | |x − y| < ǫ}. If the valuation is nonarchimedean, then this metric space or topology is rather bizarre. For instance, the open balls don’t have a unique center: in fact, if we t...

Very recently, by considering a self-mapping T on complete metric space satisfying general contractivity condition of the form ψ(d(Tx,Ty))≤φ(d(x,y)), Proinov proved some fixed-point theorems, which extended and unified many existing results in literature. Accordingly, inspired Proinov-type contraction conditions, Roldán López de Hierro et al. introduced novel family contractions fuzzy spaces (i...

In this paper, employing the common property ($E.A$), we prove a common fixed theorem for weakly compatible mappings via an implicit relation in Intuitionistic fuzzy metric space. Our results generalize the results of S. Kumar [S. Kumar, {it Common fixed point theorems in Intuitionistic fuzzy metric spaces using property (E.A)}, J. Indian Math. Soc., 76 (1-4) (2009), 94--103] and C. Alaca et al...

We provide fuzzy quasi-metric versions of a fixed point theorem ofGregori and Sapena for fuzzy contractive mappings in G-complete fuzzy metricspaces and apply the results to obtain fixed points for contractive mappingsin the domain of words.

In this paper, we shall establish some fixed point theorems for mappings with the contractive  condition of integrable type on complete intuitionistic fuzzy metric spaces $(X, M,N,*,lozenge)$. We also use Lebesgue-integrable mapping to obtain new results. Akram, Zafar, and Siddiqui introduced the notion of $A$-contraction mapping on metric space. In this paper by using the main idea of the work...

Recently, Dubickas and Smyth constructed and examined the metric Mahler measure and the metric näıve height on the multiplicative group of algebraic numbers. We give a non-Archimedean version of the metric Mahler measure, denoted M∞, and prove that M∞(α) = 1 if and only if α is a root of unity. We further show that M∞ defines a projective height on Q × /Tor(Q) as a vector space over Q. Finally,...

In a fuzzy metric space (X;M; *), where * is a continuous t-norm,a locally fuzzy contraction mapping is de ned. It is proved that any locally fuzzy contraction mapping is a global fuzzy contractive. Also, if f satis es the locally fuzzy contractivity condition then it satis es the global fuzzy contrac-tivity condition.