Riemannian manifolds have been widely employed for video representations in visual classification tasks including videobased face recognition. The success mainly derives from learning a discriminant Riemannian metric which encodes the non-linear geometry of the underlying Riemannian manifolds. In this paper, we propose a novel metric learning framework to learn a distance metric across a Euclid...

An internal characterization of metric spaces which are absolute Borel sets of multiplicative classes is given. This characterization uses complete sequences of covers, a notion introduced by Froĺık for characterizing Čechcomplete spaces. We also show that the absolute Borel class of X is determined by the uniform structure of the space of continuous functions Cp(X); however the case of absolut...

in this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. also, we give anew generalization of the mazur-ulam theorem when $x$ is a $2$-fuzzy $2$%-normed linear space or $im (x)$ is a fuzzy $2$-normed linear space, thatis, the mazur-ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...

We study the problem of approximating a function from a separable metric space D to a separable metric space Z by functions g from D to Z which have the property there is no set E of power 2** such that g is a homeomorphism of E onto g(E). Theorem 1 asserts that any one to one function may be approximated by such a function. Numerous continuous functions may be approximated by such functions wh...

in this paper, we prove some common fixed point results for two self mappingsf and g on s-metric space such that f is a g.w.c.m with respect to g.

Considering the increasing interest in fuzzy theory and possible applications,the concept of fuzzy metric space concept has been introduced by severalauthors from different perspectives. This paper interprets the theory in termsof metrics evaluated on fuzzy numbers and defines a strong Hausdorff topology.We study interrelationships between this theory and other fuzzy theories suchas intuitionis...

Banach's contraction principle has been improved and extensively studied on several generalized metric spaces. Recently, complex-valued $S$-metric spaces have been introduced and studied for this purpose. In this paper, we investigate some generalized fixed point results on a complete complex valued $S$-metric space. To do this, we prove some common fixed point (resp. fixed point) theorems usin...