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Multi-valued contraction mappings in generalized metric spaces. (English) Zbl 0192.59802

##### MSC:
 54C60 Set-valued maps (general topology) 54H25 Fixed-point and coincidence theorems in topological spaces
topology
##### References:
 [1] S. Banach,Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math.3 (1922), 133–181. [2] J. B. Diaz and B. Margolis,A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc.,74 (1968), 305–309. · Zbl 0157.29904 · doi:10.1090/S0002-9904-1968-11933-0 [3] M. Edelstein,An extension of Banach’s contraction principle, Proc. Amer. Math. Soc.,12 (1961), 7–10. [4] C. F. K. Jung,On generalized complete metric spaces, Bull. Amer. Math. Soc.,75 (1969), 113–116. · Zbl 0194.23801 · doi:10.1090/S0002-9904-1969-12165-8 [5] W. A. J. Luxemburg,On the convergence of successive approximations in the theory of ordinary differential equations, II, Koninkl. Nederl. Akademie van Wetenschappen, Amsterdam, Proc. Ser.A(5), 61, and Indag. Math. (5), 20 (1958), 540–546. [6] S. B. Nadler, Jr.,Multi-valued contraction mappings, Notices Amer. Math. Soc.,14 (1967), 930. [7] S. B. Nadler, Jr.,Multi-valued contraction mappings, Pacific J. Math.,30 (1969), 415–487.