Some Fixed Point Results on Generalized Metric Spaces

Abstract

In this thesis, someo xedopoint results have beenoproved forosingle andomulti valued mappings with the condition ofoextendedob-metricospace andocontrolledometric space, which generalizes Banach xed point theorem, Nadler's xed point theorem, and many other xed point results in the setting of these generalized metric spaces. Furthermore, we introduce Hausdor controlled metric on the class of nonempty closed subsets of controlled metric space and prove some xed point results on such spaces. Also we de ne fuzzy set, fuzzy mapping, multivaluedofuzzy contractionomappings and prove related -fuzzyo xed point results in the setting ofoextended b-metric spaces, that generalize many pre existing results in the literature. Moreover, we derive some common -fuzzy xed point results for fuzzy mappings under generalized almost z-contractions in the background of controlled metric space. As an application, some multi valued xed point results have been established. Lastly, theoconcept ofocontrolledorectangular metric space has been introduced, that generalizeoextended rectangular b-metricospace andorectangular metric space in the framework of controlled rectangular metric space, and some xed point results over such spaces have been proved. As an application, weoprove theoexistence andouniqueness ofosolution for theoFredholmointegraloequation.