Fixed Point Theorems for Monotone Generalized Contractions in Partially Ordered Metric Spaces and Applications to Integral Equations

Jackie Harjani; Kishin Sadarangani

Abstract

The purpose of this paper is to present some fixed point theorems for monotone generalized contractions in a complete metric space endowed with a partial order. Some results of J. J. Nieto and R. Rodríguez-López ["Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations", Order 22 (2005) 223-239] and of D. O'Regan and A. Petrusel ["Fixed point theorems for generalized contractions in ordered metric spaces", J. Math. Anal. Appl. 341 (2008) 1241-1252] can be obtained as particular cases of our theorems. An application to integral equations is presented in order to illustrate our results.

Author information

Contact details are reproduced from the original publication and may be historical.

Jackie Harjani

Dep. de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain

jharjani@dma.ulpgc.es

Kishin Sadarangani

Dep. de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain

ksadaran@dma.ulpgc.es

Keywords

Monotone generalized mapping
partially ordered set
altering distance function

Mathematics Subject Classification

47H10

Suggested citation

J. Harjani, K. Sadarangani. “Fixed Point Theorems for Monotone Generalized Contractions in Partially Ordered Metric Spaces and Applications to Integral Equations.” Journal of Convex Analysis 19 (2012), No. 3, 853–864.