Fixed Point Theorems in Partially Ordered G-Metric Spaces

Ravi P. Agarwal, Erdal Karapınar, Donal O’Regan and Antonio Francisco Roldán-López- de-Hierro
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Ravi P. Agarwal: Texas A&M University-Kingsville, Department of Mathematics
Erdal Karapınar: Atilim University, Department of Mathematics
Donal O’Regan: National University of Ireland
Antonio Francisco Roldán-López- de-Hierro: University of Granada, Department of Quantitative Methods for Economics and Business

Chapter Chapter 5 in Fixed Point Theory in Metric Type Spaces, 2015, pp 79-105 from Springer

Abstract: 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.

Date: 2015
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DOI: 10.1007/978-3-319-24082-4_5

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