Semwal, Pushpendra; Dimri, Ramesh Chandra A Suzuki type coupled fixed point theorem for generalized multivalued mapping. (English) Zbl 1469.54184 Abstr. Appl. Anal. 2014, Article ID 820482, 8 p. (2014). Summary: We obtain a new Suzuki type coupled fixed point theorem for a multivalued mapping \(T\) from \(X \times X\) into \(\mathrm{CB}(X)\), satisfying a generalized contraction condition in a complete metric space. Our result unifies and generalizes various known comparable results in the literature. We also give an application to certain functional equations arising in dynamic programming.Editorial remark: See also [H. H. Alsulami et al., Abstr. Appl. Anal. 2014, Article ID 235731, 8 p. (2014; Zbl 1469.54049)]. Cited in 1 ReviewCited in 6 Documents MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) 54E40 Special maps on metric spaces 54E50 Complete metric spaces Citations:Zbl 1469.54049 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Suzuki, T., A generalized Banach contraction principle that characterizes metric completeness, Proceedings of the American Mathematical Society, 136, 5, 1861-1869 (2008) · Zbl 1145.54026 · doi:10.1090/S0002-9939-07-09055-7 [2] Banach, S., Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundamenta Mathematicae, 3, 133-181 (1922) · JFM 48.0201.01 [3] Kikkawa, M.; Suzuki, T., Some similarity between contractions and Kannan mappings, Fixed Point Theory and Applications, 2008 (2008) · Zbl 1162.54019 [4] Kannan, R., Some results on fixed points. II, The American Mathematical Monthly, 76, 405-408 (1969) · Zbl 0179.28203 · doi:10.2307/2316437 [5] Nadler, S. B., Multi-valued contraction mappings, Pacific Journal of Mathematics, 30, 475-488 (1969) · Zbl 0187.45002 · doi:10.2140/pjm.1969.30.475 [6] Mizoguchi, N.; Takahashi, W., Fixed point theorems for multivalued mappings on complete metric spaces, Journal of Mathematical Analysis and Applications, 141, 1, 177-188 (1989) · Zbl 0688.54028 · doi:10.1016/0022-247X(89)90214-X [7] Daffer, P. Z.; Kaneko, H., Fixed points of generalized contractive multi-valued mappings, Journal of Mathematical Analysis and Applications, 192, 2, 655-666 (1995) · Zbl 0835.54028 · doi:10.1006/jmaa.1995.1194 [8] Semenov, P. V., On fixed points of multivalued contractions, Functional Analysis and Its Applications, 36, 2, 159-161 (2002) · Zbl 1026.47040 · doi:10.1023/A:1015682926496 [9] Ćirić, L., Multi-valued nonlinear contraction mappings, Nonlinear Analysis. Theory, Methods & Applications, 71, 7-8, 2716-2723 (2009) · Zbl 1179.54053 · doi:10.1016/j.na.2009.01.116 [10] Ćirić, L. B., Fixed points for generalized multi-valued contractions, Matematički Vesnik, 9, 24, 265-272 (1972) · Zbl 0258.54043 [11] Doric, D.; Lazović, R., Some Suzuki-type fixed point theorems for generalized multivalued mappings and applications, Fixed Point Theory and Applications, 2011, article 40 (2011) · Zbl 1274.54150 [12] Gnana Bhaskar, T.; Lakshmikantham, V., Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis. Theory, Methods & Applications, 65, 7, 1379-1393 (2006) · Zbl 1106.47047 · doi:10.1016/j.na.2005.10.017 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.