Singh, S. L.; Mishra, S. N. Fixed point theorems for single-valued and multi-valued maps. (English) Zbl 1296.54093 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 6, 2243-2248 (2011). Summary: Coincidence and fixed point theorems for single-valued and multi-valued maps generalizing recent results of Suzuki and Kikkawa (see [T. Suzuki, Proc. Am. Math. Soc. 136, No. 5, 1861–1869 (2008; Zbl 1145.54026)], [M. Kikkawa and T. Suzuki, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 9, 2942–2949 (2008; Zbl 1152.54358)], and [M. Kikkawa and T. Suzuki, Fixed Point Theory Appl. 2008, Article ID 649749, 8 p. (2008; Zbl 1162.54019)]) are obtained. Various applications, including the existence of common solutions of certain functional equations are presented. Cited in 7 Documents MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) 49L20 Dynamic programming in optimal control and differential games 54C60 Set-valued maps in general topology Keywords:coincidence point; fixed point; functional equation; dynamic programming; multi-valued map Citations:Zbl 1145.54026; Zbl 1152.54358; Zbl 1162.54019 PDFBibTeX XMLCite \textit{S. L. Singh} and \textit{S. N. Mishra}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 6, 2243--2248 (2011; Zbl 1296.54093) Full Text: DOI References: [1] Suzuki, Tomonari, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136, 1861-1869 (2008) · Zbl 1145.54026 [2] Kikkawa, M.; Suzuki, Tomonari, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69, 2942-2949 (2008) · Zbl 1152.54358 [3] Kikkawa, M.; Suzuki, Tomonari, Some similarity between contractions and Kannan mappings, Fixed Point Theory Appl., 1-8 (2008), Article ID 649749 · Zbl 1162.54019 [4] Nadler, S. B., Multi-valued contraction mappings, Pacific J. Math., 80, 475-488 (1969) · Zbl 0187.45002 [5] Covitz, H.; Nadler, S. B., Multivalued contraction mappings in generalized metric spaces, Israel J. Math., 8, 5-11 (1970) · Zbl 0192.59802 [6] Nadler, S. B., Hyperspaces of Sets (1978), Marcel - Dekker: Marcel - Dekker New York · Zbl 0432.54007 [7] Goebel, K., A coincidence theorem, Bull. Acad. Polon. Sci. Sér. Sci. Math., 16, 733-735 (1968) · Zbl 0165.49801 [8] Park, S., A coincidence theorem, Bull. Acad. Polon. Sci. Sér. Sci. Math., 29, 487-489 (1981) · Zbl 0491.54039 [9] Park, S.; Bae, J. S., Extension of a fixed point theorem of Meir and Keeler, Arkiv Mat., 19, 223-228 (1981) · Zbl 0483.47040 [10] Naimpally, S. A.; Singh, S. L.; Whitfield, J. H.M., Coincidence theorems for hybrid contractions, Math. Nachr., 127, 177-180 (1988) · Zbl 0602.54049 [11] Itoh, S.; Takahashi, W., Single-valued mappings, multivalued mappings and fixed point theorems, J. Math. Anal. Appl., 59, 514-521 (1977) · Zbl 0351.47040 [12] Singh, S. L.; Mishra, S. N., Coincidences and fixed points of nonself hybrid contractions, J. Math. Anal. Appl., 256, 486-497 (2001) · Zbl 0985.47046 [13] Hadžić, O.; Gajić, Lj., Coincidence points for set-valued mappings in convex metric spaces, Univ. Novom Sadu Zb. Rad. Prirod- Mat. Fak. Ser., 16, 13-25 (1986) · Zbl 0639.54037 [14] Ćirić, Lj. B., Fixed points of generalized multivalued contractions, Mat. Vesnik, 9, 24, 265-272 (1972) · Zbl 0258.54043 [15] Rus, I. A., Fixed point theorems for multivalued mappings in complete metric spaces, Math. Japon., 20, 21-24 (1975), (special issue) [16] Jungck, G., Commuting mappings and fixed points, Amer. Math. Monthly, 83, 261-263 (1976) · Zbl 0321.54025 [17] Bellman, R., Methods of Nonlinear Analysis, Vol. II (1973), Academic Press, Inc. · Zbl 0265.34002 [18] Bhakta, P. C.; Mitra, S., Some existence theorems for functional equations arising in dynamic programming, J. Math. Anal. Appl., 98, 348-362 (1984) · Zbl 0533.90091 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.