Fixed point results for various contractions in parametric and fuzzy b-metric spaces

The notion of parametric metric spaces being a natural generalization of metric spaces was recently introduced and studied by Hussain et al. [A new approach to fixed point results in triangular intuitionistic fuzzy metric spaces, Abstract and Applied Analysis, Vol. 2014, Article ID 69-139, 16 pp]. In this paper we introduce the concept of parametric b-metric space and investigate the existence of fixed points under various contractive conditions in such spaces. As applications, we derive some new fixed point results in triangular partially ordered fuzzy b-metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results.