Fixed point theorems for generalized contractions in ordered metric spaces

D O'Regan, A Petruşel - Journal of Mathematical Analysis and Applications, 2008 - Elsevier
D O'Regan, A Petruşel
Journal of Mathematical Analysis and Applications, 2008Elsevier
The purpose of this paper is to present some fixed point results for self-generalized
contractions in ordered metric spaces. Our results generalize and extend some recent
results of ACM Ran, MC Reurings [ACM Ran, MC Reurings, A fixed point theorem in partially
ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004)
1435–1443], JJ Nieto, R. Rodríguez-López [JJ Nieto, R. Rodríguez-López, Contractive
mapping theorems in partially ordered sets and applications to ordinary differential …
The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435–1443], J.J. Nieto, R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223–239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205–2212], J.J. Nieto, R.L. Pouso, R. Rodríguez-López [J.J. Nieto, R.L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505–2517], A. Petruşel, I.A. Rus [A. Petruşel, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411–418] and R.P. Agarwal, M.A. El-Gebeily, D. O'Regan [R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.
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