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.
