The aim of the paper is to study some generalizations of weakly Kannan and weakly Chatterjea-type contractive mappings in the setting of partial metric spaces. Some important outcomes are stated and proved, extending classic fixed point and best proximity point theorems. Examples are given in order to emphasize the utility of the main results.

In this paper, we establish a coincidence and a common fixed point for a pair of weakly compatible mappings under (ψ, φ)weakly contractive condition in G-metric spaces. Our results improve and generalize the results of Khandaqji et al. [20]. We also provide an example to support our results. Moreover, we prove that these mappings satisfy Property Q.

After the definition of the concept of fuzzy metric space by some authors 1–3 , the fixed point theory on these spaces has been developing see, e.g., 4–9 . Generally, this theory on fuzzy metric space is done for contractive or contractive-type mappings see 2, 10–13 and references therein . In this paper we introduce the concept of fuzzy order ψ-contractive mappings and give two fixed point the...