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Fixed point theorems for monotone mappings on partial metric spaces. (English) Zbl 1207.54051

Summary: S. G. Matthews [Partial metric topology. Susan Andima et al. (eds.), Papers on general topology and applications. Papers from the 8th summer conference at Queens College, New York, NY, USA, June 18–20, 1992. New York, NY: The New York Academy of Sciences. Ann. N. Y. Acad. Sci. 728, 183–197 (1994; Zbl 0911.54025)] introduced a new distance \(\mu\) on a nonempty set \(X\), which is called partial metric. If (\(X,p\)) is a partial metric space, then \(p(x,x)\) may not be zero for \(x \in X\). In the present paper, we give some fixed point results on these interesting spaces.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)

Citations:

Zbl 0911.54025
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References:

[1] Matthews, SG, Partial metric topology, 183-197, (1994) · Zbl 0911.54025
[2] Valero, O, On Banach fixed point theorems for partial metric spaces, Applied General Topology, 6, 229-240, (2005) · Zbl 1087.54020
[3] Oltra, S; Valero, O, Banach’s fixed point theorem for partial metric spaces, Rendiconti dell’Istituto di Matematica dell’Università di Trieste, 36, 17-26, (2004) · Zbl 1080.54030
[4] Altun, I; Sola, F; Simsek, H, Generalized contractions on partial metric spaces, Topology and Its Applications, 157, 2778-2785, (2010) · Zbl 1207.54052
[5] Romaguera, S, A kirk type characterization of completeness for partial metric spaces, Fixed Point Theory and Applications, 2010, 6, (2010) · Zbl 1193.54047
[6] Altun, I; Simsek, H, Some fixed point theorems on dualistic partial metric spaces, Journal of Advanced Mathematical Studies, 1, 1-8, (2008) · Zbl 1172.54318
[7] Heckmann, R, Approximation of metric spaces by partial metric spaces, Applied Categorical Structures, 7, 71-83, (1999) · Zbl 0993.54029
[8] Escardó, MH, PCF extended with real numbers, Theoretical Computer Science, 162, 79-115, (1996) · Zbl 0871.68034
[9] 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
[10] Agarwal, RP; El-Gebeily, MA; O’Regan, D, Generalized contractions in partially ordered metric spaces, Applicable Analysis, 87, 109-116, (2008) · Zbl 1140.47042
[11] Altun, I; Simsek, H, Some fixed point theorems on ordered metric spaces and application, No. 2010, 17, (2010) · Zbl 1197.54053
[12] Beg, I; Butt, AR, Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Analysis: Theory, Methods & Applications, 71, 3699-3704, (2009) · Zbl 1176.54028
[13] Ciric, L; Cakić, N; Rajović, M; Ume, JS, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory and Applications, 2008, 11, (2008) · Zbl 1158.54019
[14] Harjani, J; Sadarangani, K, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Analysis: Theory, Methods & Applications, 72, 1188-1197, (2010) · Zbl 1220.54025
[15] 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
[16] Altun, I, Some fixed point theorems for single and multi valued mappings on ordered non-Archimedean fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 7, 91-96, (2010) · Zbl 1204.54025
[17] Altun, I; Miheţ, D, Ordered non-Archimedean fuzzy metric spaces and some fixed point results, No. 2010, 11, (2010) · Zbl 1191.54033
[18] Altun, I; Imdad, M, Some fixed point theorems on ordered uniform spaces, Filomat, 23, 15-22, (2009) · Zbl 1265.54151
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