×

Some fixed point theorems on ordered metric spaces and application. (English) Zbl 1197.54053

The authors prove some fixed point theorems for nondecreasing and weakly increasing operators defined on partially ordered complete metric spaces and satisfying some metric relations on comparable pairs of elements. An application to the existence of a common solution of two integral equations is given.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
45G15 Systems of nonlinear integral equations
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Ran ACM, Reurings MCB: A fixed point theorem in partially ordered sets and some applications to matrix equations.Proceedings of the American Mathematical Society 2004,132(5):1435-1443. 10.1090/S0002-9939-03-07220-4 · Zbl 1060.47056 · doi:10.1090/S0002-9939-03-07220-4
[2] Agarwal RP, El-Gebeily MA, O’Regan D: Generalized contractions in partially ordered metric spaces.Applicable Analysis 2008,87(1):109-116. 10.1080/00036810701556151 · Zbl 1140.47042 · doi:10.1080/00036810701556151
[3] Nieto JJ, Rodríguez-López R: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations.Order 2005,22(3):223-239. 10.1007/s11083-005-9018-5 · Zbl 1095.47013 · doi:10.1007/s11083-005-9018-5
[4] Nieto JJ, Rodríguez-López R: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations.Acta Mathematica Sinica 2007,23(12):2205-2212. 10.1007/s10114-005-0769-0 · Zbl 1140.47045 · doi:10.1007/s10114-005-0769-0
[5] Nieto JJ, Pouso RL, Rodríguez-López R: Fixed point theorems in ordered abstract spaces.Proceedings of the American Mathematical Society 2007,135(8):2505-2517. 10.1090/S0002-9939-07-08729-1 · Zbl 1126.47045 · doi:10.1090/S0002-9939-07-08729-1
[6] O’Regan D, Petruşel A: Fixed point theorems for generalized contractions in ordered metric spaces.Journal of Mathematical Analysis and Applications 2008,341(2):1241-1252. 10.1016/j.jmaa.2007.11.026 · Zbl 1142.47033 · doi:10.1016/j.jmaa.2007.11.026
[7] Ćirić LjB: Generalized contractions and fixed-point theorems.Publications Institut Mathématique 1971,12(26):19-26. · Zbl 0234.54029
[8] Ćirić LjB: Fixed points of weakly contraction mappings.Publications Institut Mathématique 1976, 20(34): 79-84. · Zbl 0354.54031
[9] Ćirić LjB: Common fixed points of nonlinear contractions.Acta Mathematica Hungarica 1998,80(1-2):31-38. · Zbl 0918.47045
[10] Altun I, Turkoglu D: Some fixed point theorems for weakly compatible multivalued mappings satisfying an implicit relation.Filomat 2008,22(1):13-21. 10.2298/FIL0801011A · Zbl 1199.54202 · doi:10.2298/FIL0801011A
[11] Altun I, Turkoglu D: Some fixed point theorems for weakly compatible mappings satisfying an implicit relation.Taiwanese Journal of Mathematics 2009,13(4):1291-1304. · Zbl 1194.54055
[12] Imdad M, Kumar S, Khan MS: Remarks on some fixed point theorems satisfying implicit relations.Radovi Matematički 2002,11(1):135-143. · Zbl 1033.54025
[13] Popa V: A general coincidence theorem for compatible multivalued mappings satisfying an implicit relation.Demonstratio Mathematica 2000,33(1):159-164. · Zbl 0947.54023
[14] Sharma S, Deshpande B: On compatible mappings satisfying an implicit relation in common fixed point consideration.Tamkang Journal of Mathematics 2002,33(3):245-252. · Zbl 1029.47037
[15] Turkoglu D, Altun I: A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying an implicit relation.Sociedad Matemática Mexicana. Boletín 2007,13(1):195-205. · Zbl 1171.54342
[16] Matkowski J: Fixed point theorems for mappings with a contractive iterate at a point.Proceedings of the American Mathematical Society 1977,62(2):344-348. 10.1090/S0002-9939-1977-0436113-5 · Zbl 0349.54032 · doi:10.1090/S0002-9939-1977-0436113-5
[17] Dhage BC: Condensing mappings and applications to existence theorems for common solution of differential equations.Bulletin of the Korean Mathematical Society 1999,36(3):565-578. · Zbl 0940.47043
[18] Dhage BC, O’Regan D, Agarwal RP: Common fixed point theorems for a pair of countably condensing mappings in ordered Banach spaces.Journal of Applied Mathematics and Stochastic Analysis 2003,16(3):243-248. 10.1155/S1048953303000182 · Zbl 1068.47071 · doi:10.1155/S1048953303000182
[19] Ahmad, B.; Nieto, JJ, The monotone iterative technique for three-point second-order integrodifferential boundary value problems with [InlineEquation not available: see fulltext.]-Laplacian, No. 2007, 9 (2007)
[20] Cabada A, Nieto JJ: Fixed points and approximate solutions for nonlinear operator equations.Journal of Computational and Applied Mathematics 2000,113(1-2):17-25. 10.1016/S0377-0427(99)00240-X · Zbl 0954.47038 · doi:10.1016/S0377-0427(99)00240-X
[21] Ćirić, LjB; Cakić, N.; Rajović, M.; Ume, JS, Monotone generalized nonlinear contractions in partially ordered metric spaces, No. 2008, 11 (2008) · Zbl 1158.54019
[22] Nieto JJ: An abstract monotone iterative technique.Nonlinear Analysis: Theory, Methods & Applications 1997,28(12):1923-1933. 10.1016/S0362-546X(97)89710-6 · Zbl 0883.47058 · doi:10.1016/S0362-546X(97)89710-6
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.