Contractive definitions and discontinuity at fixed point

Abstract

In this paper, we investigate some contractive definitions which are strong enough to generate a fixed point that do not force the mapping to be continuous at the fixed point. Finally, we obtain a fixed point theorem for generalized nonexpansive mappings in metric spaces by employing Meir-Keeler type conditions.<p style="-qt-paragraph-type: empty; -qt-block-indent: 0; text-indent: 0px; margin: 0px;"> </p>