In this paper, fixed point results for a newly introduced Geraghty quasi-contraction type mappings are proved in more general metric spaces called T-orbitally complete dislocated quasi-metric spaces. Geraghty quasi-contraction type mappings generalize, among others, Ciric’s quasi-contraction mappings and other Geraghty quasi-contractive type mappings in the literature. Fixed point results are obtained without imposing a continuity condition on the mapping, thereby further generalizing some other related work in the literature. An example is given to show the validity of results obtained.

In this paper, by using α-admissible mappings embedded in simulation functions, some fixed point results are proved in the setting of a Hausdorff S-complete uniform space. The results obtained generalizes and unifies some known results in the literature.

In this paper, we introduce a new concept of α-φ-Geraghty proximal quasi-contraction type mappings and establish best proximity point theorems for those mappings in proximal T-orbitally complete metric spaces. This generalizes and complements the proofs of some known fixed and best proximity point results.