×
Caballero, J.; Harjani, J.; Sadarangani, K.

Contractive-like mapping principles in ordered metric spaces and application to ordinary differential equations. (English) Zbl 1194.54057

Fixed Point Theory Appl. 2010, Article ID 916064, 14 p. (2010).
Summary: The purpose of this paper is to present a fixed point theorem for generalized contractions in partially ordered complete metric spaces. We also present an application to first-order ordinary differential equations.

Cited in 20 Documents

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
34A99 General theory for ordinary differential equations
PDF BibTeX XML Cite
\textit{J. Caballero} et al., Fixed Point Theory Appl. 2010, Article ID 916064, 14 p. (2010; Zbl 1194.54057)
Full Text: DOI EuDML
  • logo of hbz
  • logo of WorldCat

References:

[1] Agarwal, RP; El-Gebeily, MA; O’Regan, D, Generalized contractions in partially ordered metric spaces, Applicable Analysis, 87, 109-116, (2008) · Zbl 1140.47042
[2] Amini-Harandi, A; Emami, H, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Analysis: Theory, Methods & Applications, 72, 2238-2242, (2010) · Zbl 1197.54054
[3] Burgić, D; Kalabušić, S; Kulenović, MRS, Global attractivity results for mixed-monotone mappings in partially ordered complete metric spaces, No. 2009, 17, (2009) · Zbl 1168.54327
[4] Ćirić, L; Cakić, N; Rajović, M; Ume, JS, Monotone generalized nonlinear contractions in partially ordered metric spaces, No. 2008, 11, (2008) · Zbl 1158.54019
[5] Gnana Bhaskar, T; Lakshmikantham, V, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis: Theory, Methods & Applications, 65, 1379-1393, (2006) · Zbl 1106.47047
[6] Harjani, J; Sadarangani, K, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Analysis: Theory, Methods & Applications, 71, 3403-3410, (2009) · Zbl 1221.54058
[7] Harjani, J; Sadarangani, K, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Analysis: Theory, Methods & Applications, 71, 3403-3410, (2009) · Zbl 1221.54058
[8] Lakshmikantham, V; Ćirić, L, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis: Theory, Methods & Applications, 70, 4341-4349, (2009) · Zbl 1176.54032
[9] Nieto, JJ; Rodríguez-López, R, Existence of extremal solutions for quadratic fuzzy equations, Fixed Point Theory and Applications, 2005, 321-342, (2005) · Zbl 1102.54004
[10] Nieto, JJ; Rodríguez-López, R, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 223-239, (2005) · Zbl 1095.47013
[11] Nieto, JJ; Rodríguez-López, R, Applications of contractive-like mapping principles to fuzzy equations, Revista Matemática Complutense, 19, 361-383, (2006) · Zbl 1113.26030
[12] Nieto, JJ; Pouso, RL; Rodríguez-López, R, Fixed point theorems in ordered abstract spaces, Proceedings of the American Mathematical Society, 135, 2505-2517, (2007) · Zbl 1126.47045
[13] Nieto, JJ; Rodríguez-López, R, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Mathematica Sinica, 23, 2205-2212, (2007) · Zbl 1140.47045
[14] O’Regan, D; Petruşel, A, Fixed point theorems for generalized contractions in ordered metric spaces, Journal of Mathematical Analysis and Applications, 341, 1241-1252, (2008) · Zbl 1142.47033
[15] Petruşel, A; Rus, IA, Fixed point theorems in ordered [inlineequation not available: see fulltext.]-spaces, Proceedings of the American Mathematical Society, 134, 411-418, (2006) · Zbl 1086.47026
[16] Ran, ACM; Reurings, MCB, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proceedings of the American Mathematical Society, 132, 1435-1443, (2004) · Zbl 1060.47056
[17] Wu, Y, New fixed point theorems and applications of mixed monotone operator, Journal of Mathematical Analysis and Applications, 341, 883-893, (2008) · Zbl 1137.47044
[18] Cabada, A; Nieto, JJ, Fixed points and approximate solutions for nonlinear operator equations, Journal of Computational and Applied Mathematics, 113, 17-25, (2000) · Zbl 0954.47038
[19] Geraghty, MA, On contractive mappings, Proceedings of the American Mathematical Society, 40, 604-608, (1973) · Zbl 0245.54027
[20] Babu, GVR; Lalitha, B; Sandhya, ML, Common fixed point theorems involving two generalized altering distance functions in four variables, Proceedings of the Jangjeon Mathematical Society, 10, 83-93, (2007) · Zbl 1139.54321
[21] Naidu, SVR, Some fixed point theorems in metric spaces by altering distances, Czechoslovak Mathematical Journal, 53, 205-212, (2003) · Zbl 1013.54011
[22] Sastry, KPR; Babu, GVR, Some fixed point theorems by altering distances between the points, Indian Journal of Pure and Applied Mathematics, 30, 641-647, (1999) · Zbl 0938.47044
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.