we obtain two fixed point theorems for a kind of $varphi $-contractions incomplete fuzzy metric spaces, which are applied to easily deduceintuitionistic versions that improve and simplify the recent results of x.huang, c. zhu and x. wen.

This is a partial account of the fascinating history of Distance Geometry. We make no claim to completeness, but we do promise a dazzling display of beautiful, elementary mathematics. We prove Heron’s formula, Cauchy’s theorem on the rigidity of polyhedra, Cayley’s generalization of Heron’s formula to higher dimensions, Menger’s characterization of abstract semi-metric spaces, a result of Gödel...

We introduce a class of metric perceptual distances between textures. The first metric is sensitive to both rotation and scale differences, and provides a basis for two other metrics, one invariant to rotation, and the other invariant to both rotation and scale. Our metrics are based on Earth Mover’s Distance computations on log-polar distributions of spatial frequency computed from Gabor filte...

We propose to solve a text categorization task using a new metric between documents, based on a priori semantic knowledge about words. This metric can be incorporated into the definition of radial basis kernels of Support Vector Machines or directly used in a K-nearest neighbors algorithm. Both SVM and KNN are tested and compared on the 20 newsgroups database. Support Vector Machines provide th...

In this work‎, ‎we formulate Chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. We also discuss the uniqueness of the fixed point. The given result is a generalization of Chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a graph.

In this paper, we introduce a new class of implicit functions and also common property (E.A) in modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces besides discussing related results and illustrative examples. We are not aware of any paper dealing with such implicit functions in modified intuit...

Quantum chemical computational procedures, like LCAOMO theory and quantum similarity, use non orthogonal function basis sets, which define finite dimensional subspaces of a Hilbert space. Based on the original overlap metric matrices, generated by the chosen finite non orthogonal basis sets, there are several symmetrical overlap and basis set transformations possible. This study tries to find o...

In this paper we define a discrete subset family of a topological space and basis sigma locally finite and sigma discrete. First, we prove an auxiliary fact for discrete family and sigma locally finite and sigma discrete basis. We also show the necessary condition for the Nagata Smirnov theorem: every metrizable space is T3 and has a sigma locally finite basis. Also, we define a sufficient cond...