Fixed Point Theorems in Fuzzy Abstract Spaces


In this dissertation, the notion of fuzzy rectangular-b-metric space is introduced, which generalizes the notions of a fuzzy metric space and a fuzzy b-metric space. Well known xed point theorems are established in the setting of fuzzy rectangular b-metric spaces and illustrated by an example. Also by introducing the concept of extended fuzzy b-metric space, a Banach-type xed point theorem in the setting of this more general class of fuzzy metric spaces is proved. The notion of Hausdor extended fuzzy b-metric space is also studied and certain xed point results for some multivalued contractions in the setting of G-complete extended fuzzy b-metric space are also established. Some examples are furnished which illustrate main results. As applications of main results, xed point results involving fuzzy integral inequalities and fuzzy integral inclusion are established. These results extend and generalize many existing results in literature.

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