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Fixed point theorems for single-valued and multi-valued maps. (English) Zbl 1296.54093

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.

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
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References:

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