In this work, we prove the existence of best proximity point results for ⊥-contraction (orthogonal-contraction) mappings on an O-complete metric space (orthogonal-complete space). Subsequently, these are employed to establish common result. Finally, provide suitable examples demonstrate validity our results.

The intent of the paper is to study semi-cyclic type contraction condition for a pair of maps (S, T). Our aim is to establish an existence theorem for common fixed points and best proximity points for such a pair in Banach spaces. The results obtained herein extend some recent results.

In this paper, we prove fixed point theorem for φ − H contraction in fuzzy metric space in sense of George and Veeramani.