Journal of Convex Analysis 19 (2012), No. 3, 853--864
Copyright Heldermann Verlag 2012
Fixed Point Theorems for Monotone Generalized Contractions in Partially Ordered Metric Spaces and Applications to Integral Equations
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
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.
Keywords: Monotone generalized mapping, partially ordered set, altering distance function.
MSC: 47H10
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