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

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.