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The coincidence problem for compositions of set-valued maps

  • H. Ben-El-Mechaiekh (a1)
Abstract

The main purpose of this work is to give a general and elementary treatment of the fixed point and the coincidence problems for compositions of set-valued maps with not necessarily locally convex domains and to display, once more, the central rôle played by the selection property.

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[1]G. Allen , ‘Variational inequalities, complementarity problems and duality theorems’, J. Math. Anal. Appl. 58 (1977), 110.

[2]J.P. Aubin and A. Cellina , Differential inclusion (Springer-Verlag, Berlin, Heidelberg, New York, 1984).

[8]F.E. Browder , ‘The fixed point theory of multi-valued mappings in topological vector spaces’, Math. Ann. 177 (1968), 283301.

[9]J. Dugundji , ‘An extension of Tietze's theorem’, Pacific J. Math. (1951), 353367.

[11]K. Fan , ‘Fixed point and minimax theorems in locally convex topological linear spaces’, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 121126.

[12]K. Fan , ‘Some properties of convex sets related to fixed point theorems’, Math. Ann. 266 (1984), 519537.

[18]C.W. Ha , ‘Minimax and fixed point theorems’, Math. Ann. 248 (1980), 7377.

[19]O. Hanner , ‘Retraction and extension of mappings of metric and non-metric spaces’, Ark.Mat. 2 (1952), 315360.

[21]S. Kakutani , ‘A generalization of Brouwer's fixed point theorem’, Duke Math. J. 8 (1941), 457459.

[22]V. Klee , ‘Leray-Schauder theory without local convexity’, Math. Ann. 141 (1960), 286296.

[23]M. Lassonde , ‘On the use of KKM multifunctions in fixed point theory and related topics’, J. Math. Anal. Appl 97 (1983), 151201.

[25]B. Michael , ‘Continuous selections’, Ann. of Math. 63 (1956), 361382.

[29]B. Tarafdar , ‘A fixed point theorem equivalent to Fan-Knaster-Kuratowski Mazurkiewicz's theorem’, J. Math. Anal. Appl. 128 (1987), 475479.

[31]L. Vietoris , ‘Ueber den höheren zusammenhang kompakier raume und eine kiasse von zusammenhangstrenen abbidungen’, Math. Ann. 97 (1927), 454472.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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