conditionally compatible mappings, non-compatible mappings, faintly compatible mappings and some results on common fixed point in c∗-algebra valued metric space

This manuscript introduces and investigates various types of mappings in the context of a c ∗-algebra valued metric space. these include conditionally compatible, non-compatible, and faintly compatible mappings. additionally, the manuscript establishes fixed-point results for certain combinations of these mappings. specifically, it considers pairs of self-mappings that satisfy either a (ϕ−ψ)-kannan-type or chatterjea-type contractive condition and proves common fixed point theorems for faintly compatible continuous or reciprocal continuous along with non-compatible pairs of such mappings. also, non-compatibility is relaxed by using the e.a. property and faintly compatible continuous property or reciprocal continuous property for pairs of self-mappings. to demonstrate the practicality of these results, the manuscript includes examples that illustrate their usefulness.