ABSTRACT
A common point theorem ensures the existence of a common fixed point of a pair of mappings under suitable assumptions on the space and on the mappings. Those assumptions are sufficient and include conditions of commutativity, containment of ranges of mappings. Continuity of at least one mapping or weaker notion, contractivity, and all substantial common fixed point theorem attempts to obtain or soften required values of one of more such conditions. In addition to ensuring existence of a common point, it may be necessary to prove its uniqueness. From a computational view, a constructive algorithm to calculate the value of a common fixed point is desirable. Such algorithms often require iterates of the given mappings. The existence, uniqueness and approximations of common fixed points are important features of the common point theorem. The Banach contraction principle for single mapping and Jungck's common fixed point theorem for a pair of mappings cover all three features convincingly.
