Harjani, J.; Rocha, J.; Sadarangani, K. Generalized coupled fixed points and its application to a class of systems of functional equations arising in dynamic programming. (English) Zbl 1410.90235 Appl. Math. Comput. 268, 839-843 (2015). Summary: In this paper, we introduce the definition of generalized coupled fixed point in the space of the bounded functions on a set \(S\) and we prove a result about the existence and uniqueness of such points. As an application of our result, we study the problem of existence and uniqueness of solutions for a class of systems of functional equations which appears in dynamic programming. Cited in 1 Document MSC: 90C39 Dynamic programming 65K05 Numerical mathematical programming methods 47H10 Fixed-point theorems Keywords:coupled fixed point; functional equation; dynamic programming PDFBibTeX XMLCite \textit{J. Harjani} et al., Appl. Math. Comput. 268, 839--843 (2015; Zbl 1410.90235) Full Text: DOI References: [1] Rhoades, B. E., Some theorems on weakly contractive maps, Nonlinear Anal., 47, 2683-2693 (2001) · Zbl 1042.47521 [2] Abbas, M.; Sintunavarat, W.; Kumam, P., Coupled fixed point of generalized contractive mappings on partially ordered G-metric spaces, Fixed Point Theory Appl., 2012, 31 (2012) · Zbl 1469.54028 [3] Agarwal, R.; Sintunavarat, W.; Kumam, P., Coupled coincidence point and common coupled fixed point theorems with lacking the mixed monotone property, Fixed Point Theory Appl., 2013, 22 (2013) · Zbl 1295.54039 [4] Sintunavarat, W.; Kumam, P., Coupled fixed point results for nonlinear integral equations, J. Egypt. Math. Soc., 21, 266-272 (2013) · Zbl 1527.54067 [5] Sintunavarat, W.; Radenovic, S.; Golubovic, Z.; Kumam, P., Coupled fixed point theorems for F-invariant set and applications, Appl. Math. Inf. Sci., 7, 247-255 (2013) [6] Kadelburg, Z.; Kuman, P.; Radenovic, S.; Sintunavarat, W., Commom coupled fixed point theorems for Geraghty’s type contraction mappings using monotone preperty, Fixed Point Theory Appl., 2015, 27 (2015) [7] Bellman, R.; Lee, E. S., Functional equations in dynamic programming, Aequ. Math., 17, 1-18 (1978) · Zbl 0397.39016 [8] Liu, Z.; Agarwal, R. P.; Kang, S. M., On solvability of functional equations and system of functional equations arising in dynamic programming, J. Math. Anal. Appl., 297, 111-130 (2004) · Zbl 1055.39038 [9] Liu, Z.; Ume, J. S.; Kang, S. M., Some existence theorems for functional equations and system of functional equations arising in dynamic programming, Taiwan. J. Math., 14, 1517-1536 (2010) · Zbl 1215.49008 [10] Deepmala, Existence theorems for solvability of a functional equation arising in dynamic programming, Int. J. Math. Sci., 2014, 9 (2014) · Zbl 1286.39018 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.