Abstract:
Banach contraction principle is one of the most famous results in the literature of xed point theory and has provided the basis for metric xed point theory. This result provides us a systematic way to nd xed point of a self mapping. Nadler extended the Banach contraction principle to multi valued mappings using the concept of Hausdor metric spaces. The purpose of this dissertation is to introduce some more generalized results in the literature of metric xed point theory. We introduce xed point theorems for both single and multi valued mappings satisfying the weaker form of contraction conditions on the structure of metric spaces as well as some abstract spaces like, partial metric spaces, uniform spaces, gauge spaces and b-metric spaces.
