Fixed point theorems in M-metric spaces

In this master of science thesis, some fixed point results for Klim-Wardowski type multivalued mappings in M-metric spaces have been obtained. Thus, the Banach contraction principle, which is accepted as the beginning of fixed point theory in metric spaces and has a significant application area in various sciences as well as mathematics, has been extended to include fixed point results for multivalued mappings existing in the literature. Hence, first, the fixed point studies obtained for multivalued mappings in metric spaces have been reminded. Then, recalling the definition and some properties of M-metric spaces, the fixed point result obtained for Feng-Liu type set-valued transformations in these spaces has been given without proof. Finally, our main result for Klim-Wardowski type mixed multivalued mappings has been expressed and proved. Also, the result obtained in this section has been supported by an important example.