Compatible Mappings and Its Various Variants in Metric Space

A study on compatible mappings becomes necessary to do research on multiple self-mappings to find the fixed points, called common fixed points in fixed point theory. To obtain the weaker forms of commuting mappings [16], G. Jungck introduced the notion of compatible mappings [18] in metric space in 1986. This article presents a study on compatible mappings and their various variants of non-commuting map pings in metric space and verifies its relationship through examples. It facilitates comparative analysis and strengthens the relationship between them.