A study of k- Contraction and the Triangular a Orbital Admissibility Condition in Quasi-metric Space

Abstract

Objective: To establish the presence of fixed point under a novel contraction condition and a freshly defined distance function, we harness the concept of triangular α orbital admissible mappings. Method: Consider two mapping in quasi-metric space. These two mapping satisfy a new contraction condition and also the triangular αorbital admissible condition. Define the sequences for two mappings. Consider two cases for odd and even sequences. Show that a fixed point is common for two mappings and then demonstrate its uniqueness. Findings: Unique common fixed point exists. Novelty: A new technique is used, so the length of proof become very short as compare to theorems available in literature.