A new approach to metrical fixed point theorems

Abstract In this paper, we present new conditions yielding a unique fixed point for non expansive type mappings. We also obtain common fixed point theorems for mappings that not necessarily satisfy any known contractive type conditions. Since general methods for studying common fixed points of non-contractive mappings are not available, our present findings provides a new tools in this direction. Moreover, a common fixed point theorem is used to demonstrate in solving nonlinear integral equation problem.