Geodesic
Fixed Point Theorems for Monotone Generalized Contractions in Partially Ordered Metric Spaces and Applications to Integral Equations
Journal of convex analysis, Tome 19 (2012) no. 3, pp. 853-864

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 47H10
Mots-clés : Monotone generalized mapping, partially ordered set, altering distance function 
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     author = {J. Harjani and K. Sadarangani},
     title = {Fixed {Point} {Theorems} for {Monotone} {Generalized} {Contractions} in {Partially} {Ordered} {Metric} {Spaces} and {Applications} to {Integral} {Equations}},
     journal = {Journal of convex analysis},
     pages = {853--864},
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     volume = {19},
     number = {3},
     year = {2012},
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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, Tome 19 (2012) no. 3, pp. 853-864. http://geodesic.mathdoc.fr/item/JCA_2012_19_3_JCA_2012_19_3_a11/