In this article, we introduce concepts of Pompeiu-Hausdorff bipolar metric, multivalued covariant and contravariant contraction mappings in bipolar metric spaces. In addition to these, we express two main fixed point theorems, which are supported with four important corollaries, related to these multivalued mappings. Finally we give an example which presents the applicability of our obtained results.

In this article, we introduce the notion of commutativity for covariant and contravariant mappings in bipolar metric spaces. Afterwards, by using this notion, we prove some common fixed point theorems which show the existence and uniqueness of common fixed point for covariant and contravariant mappings satisfying contractive type conditions.

We introduce a new fixed point theorem on complete metric spaces, which generalizes some former results, and we apply this to obtain a surjectivity theorem for Gâteaux differentiable mappings between Banach spaces.

In this paper, we give some new fixed point results over bipolar metric spaces, that extend Caristi's and Downing-Kirk's fixed point theorems.

In this paper, we introduce functionally generalized normed spaces as a generalization of G  metric spaces and normed spaces. Some constructions are described within this structure and some related results are obtained.