In this paper, the notion of $psi -$weak contraction cite{Rhoades} isextended to fuzzy metric spaces. The existence of common fixed points fortwo mappings is established where one mapping is $psi -$weak contractionwith respect to another mapping on a fuzzy metric space. Our resultgeneralizes a result of Gregori and Sapena cite{Gregori}.

In this paper is introduced a new type of generalization of metric spaces called $S_b$ metric space. For this new kind of spaces it has been proved a common fixed point theorem for four mappings which satisfy generalized contractive condition. We also present example to confirm our theorem.

Let $(X,d)$ be an infinite compact metric space, let $(B,parallel . parallel)$ be a unital Banach space, and take $alpha in (0,1).$ In this work, at first we define the big and little $alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $alpha$-lipschitz $B$-valued operator algebra, $lip_{alpha}(X,B)$. Then we characterize its second dual space.

We consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let X and Y be two smooth vector fields on a two-dimensional manifold M . If X and Y are everywhere linearly independent, then they define a classical Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become l...

By local isometries we mean mappings which locally preserve distances. A few of the main results are: 1. For each local isometry / of a compact metric space (M,p) into itself there exists a unique decomposition of M into disjoint open sets, M = Ai g U • • • U Ai>, (0 < n < oo) such that (i) f(M}0) = M!Q, and (ii) f(M{) C M{_x and M< ^ 0 for each i, 1 < i < n. 2. Each local isometry of a metric ...

— Let X and Y be two smooth vector fields on a two-dimensional manifold M . If X and Y are everywhere linearly independent, then they define a Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become linearly dependent somewhere on M , then the corresponding Riemannian metric has singularities, but under generic condi...

In recent years, the study of partial differential equations on self-similar fractals has attracted increasing interest (see, for example, [7–9, 13, 14]). We investigate a class of nonlinear diffusions with source terms on general metric measure spaces. Diffusion is of fundamental importance in many areas of physics, chemistry and biology. Applications of diffusion include sintering, i.e. makin...

This study involves new notions of continuity mapping between quasi-cone metrics spaces (QCMSs), cone metric (CMSs), and vice versa. The relation all were thoroughly studied supported with the help examples. In addition, these continuities compared various types two QCMSs. are

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,...