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A fixed point theorem for a system of multivalued transformations


Author: S. Czerwik
Journal: Proc. Amer. Math. Soc. 55 (1976), 136-139
MathSciNet review: 0394619
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Abstract | References | Additional Information

Abstract: We shall prove a fixed point theorem for a system of multivalued mappings which generalizes the result obtained by the author [1, Theorem 1]. For $ n = 1$ we obtain a generalization of results of Reich [5, Theorem 5] and Nadler [3, Theorem 5], [4, Theorem 1].


References [Enhancements On Off] (What's this?)

  • [1] S. Czerwik, Fixed point theorems for system multi-valued mappings, Coll. Math. (to appear).
  • [2] J. Matkowski, Some inequalities and a generalization of Banach’s principle, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 21 (1973), 323–324 (English, with Russian summary). MR 0317116
  • [3] Sam B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475–488. MR 0254828
  • [4] Sam B. Nadler Jr., Some results on multi-valued contraction mappings, Set-Valued Mappings, Selections and Topological Properties of 2^{𝑥} (Proc. Conf., SUNY, Buffalo, N.Y., 1969) Lecture Notes in Mathematics, Vol. 171, Springer, Berlin, 1970, pp. 64–69. MR 0275391
  • [5] Simeon Reich, Kannan’s fixed point theorem, Boll. Un. Mat. Ital. (4) 4 (1971), 1–11. MR 0305163


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0394619-0
Keywords: Multivalued mappings, iteration, fixed point theorems
Article copyright: © Copyright 1976 American Mathematical Society