For a given metric space (S, d), let us use the term “standard σ-field” to denote the σ-field S of subsets of S generated by the open balls (in the metric d). A function f : S×S×S× . . .→ S is “measurable” (with respect to S) if for every set A ∈ S one has that f−1(A) is a member of S×S×S×. . . , the product σ-field on S × S × S × . . . . Suppose B is a separable real Banach space. Suppose (Ω,F...

Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...

in this paper we study the relationships existing between total measurability in variation and gould type fuzzy integrability (introduced and studied in [21]), giving a special interest on their behaviour on atoms and on finite unions of disjoint atoms. we also establish that any continuous real valued function defined on a compact metric space is totally measurable in the variation of a regula...

In this paper, following the ideas of (continuous) t-norm and interval numbers, a concept of (continuous) interval-valued t-norm is proposed. Based on the interval-valued fuzzy set and the continuous interval-valued t-norm, we propose a notion of interval-valued fuzzy metric space, which is a generalization of fuzzy metric space in the sense of George and Veeramani [Fuzzy Sets and Systems 64 (1...

We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...

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 prove a common fixed point theorem for six mappings (two set valued and four single valued mappings) without assuming compatibility and continuity of any mapping on non complete metric spaces. to prove the theorem, we use a non compatible condition, that is, weak commutativity of type (kb). we show that completeness of the whole space is not necessary for the existence and uni...

‎ Let $(X,d)$ be a metric space and $Jsubseteq (0,infty)$ be a nonempty set. We study the structure of the arbitrary intersection of vector-valued Lipschitz algebras, and define a special Banach subalgebra of $cap{Lip_gamma (X,E):gammain J}$, where $E$ is a Banach algebra, denoted by $ILip_J (X,E)$. Mainly, we investigate $C-$character amenability of $ILip_J (X,E)$.