Bipolar Multiplicative Metric Spaces and Fixed Point Theorems of Covariant and Contravariant Mappings

The definition of bipolar multiplicative metric space is introduced in this article, and in this space some properties are derived. Multiplicative contractions for covariant and contravariant maps are defined and fixed points are obtained. Also, some fixed point results of covariant and contravariant maps satisfying multiplicative contraction conditions are proved for bipolar multiplicative metric spaces. Moreover, Banach contraction principle and Kannan fixed point theorem are generalized.

Keywords:

Bipolar multiplicative metric space , multiplicative contraction , Fixed point.