ANALYSIS AND PDE ON METRIC MEASURE SPACES: SOBOLEV FUNCTIONS AND VISCOSITY SOLUTIONS Xiaodan Zhou, PhD University of Pittsburgh, 2016 We study analysis and partial differential equations on metric measure spaces by investigating the properties of Sobolev functions or Sobolev mappings and studying the viscosity solutions to some partial differential equations. This manuscript consists of two par...

Partial metrics constitute a generalization of classical for which self-distance may not be zero. They were introduced by S.G. Matthews in 1994 order to provide an adequate mathematical framework the denotational semantics programming languages. Since then, different works devoted obtaining counterparts metric fixed-point results more general context partial metrics. Nevertheless, literature wa...

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...

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.