Introduction Sessa [9] generalized the notion of commuting maps given by Jungck [2] and introduced weakly commuting mappings. Further, Jungck [3] introduced more generalized commutativity called compatibility. In 1998, Jungck and Rhoades [4] introduced the notion of weakly compatible maps and showed that compatible maps are weakly compatible but converse need not true. Menger [5] introduced the...

In the last years, fixed point theorems have been applied to show the existence and uniqueness of the solutions of differential equations, integral equations and many other branches mathematics see, e.g., 1–3 . Some common fixed point theorems for weakly commuting, compatible, δ-compatible and weakly compatible mappings under different contractive conditions in metric spaces have appeared in 4–...

Fixed points are also called as invariant points. Invariant point theorems very essential tools in solving problems arising different branches of mathematical analysis. In the present paper, we establish three unique common using two self-mappings, four self-mappings and six bicomplex valued metric space. first theorem, generate a theorem for by weaker conditions such weakly compatible, general...