AbstractThe study of fixed-point theory has been an essential part of nonlinear functional analysis, with significant applications in optimization, approximation theory, and differential equations. While classical results have largely focused on self-mappings, the investigation of fixed points for non-self-mappings opens new avenues in nonlinear analysis. This paper establishes new common fixed-point theorems for pairs of non-self-mappings defined on metrically convex spaces. By introducing contractive conditions and compatibility assumptions, we extend and generalize several known results in fixed point theory. Examples are provided to illustrate the applicability of the proposed theorems.
Rajak et al. (Wed,) studied this question.