On Common Fixed Points Of Set Valued Maps On Metric Spaces With Graph And Applications

Abstract

In this thesis, we derive some common fixed point results for set-valued generalized newlinecontractions on a metric space with graph and its applications, Mizoguchi-Takahashi local newlinecontractions is actually a Feng-Liu contractions on a metrically convex space, and fixed newlinepoints for uniformly local asymptotic contractions. newlineWe establish the occurrence of common fixed points and coincidence points for a couple of newlinesingle valued and set-valued mappings on a metric space having graphical structure involving newlinethe Hausdorff distance function. This result in fact extends the Kamran s result regarding newlinethe presence of common fixed points on metric space. Further, we ensure the presence newlineof common fixed points for a pair of single valued and set-valued mappings on a metric newlinespace having graphical structure without involving the Hausdorff distance function. As an newlineimplementation of our results, we deduce sufficient criteria for the occurrence of a solution newlinefor the Caputo fractional differential equation. An invariant best approximation result on a newlinenormed linear space is derived from our results. By applying our theorem, we deduce the newlineconvergence of the iterates for a nonlinear q-analogue Bernstein operator.