Fixed Point Theorems in Partially Ordered G-Metric Spaces

Abstract

In [168], Ran and Reurings established a fixed point theorem that extends the Banach contraction principle to the setting of partially ordered metric spaces (see Theorem A.1.1). In their original version, Ran and Reurings used a continuous function. Nieto and Rodríguez-López established a similar result replacing the continuity of the nonlinear operator by a property on the partially ordered metric space (see Theorem A.1.2). In this chapter, we present some fixed point theorems in the setting of partially ordered G-metric spaces. In particular, we will use a binary relation weaker than a partial order.