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New versions on Nikaidô's coincidence theorem

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EN
In 1959, Nikaidô established a remarkable coincidence theorem in a compact Hausdorff topological space, to generalize and to give a unified treatment to the results of Gale regarding the existence of economic equilibrium and the theorems in game problems. The main purpose of the present paper is to deduce several generalized key results based on this very powerful result, together with some KKM property. Indeed, we shall simplify and reformulate a few coincidence theorems on acyclic multifunctions, as well as some Górniewicz-type fixed point theorems. Beyond the realm of monotonicity nor metrizability, the results derived here generalize and unify various earlier ones from the classic optimization theory. In the sequel, we shall deduce two versions of Nikaidô's coincidence theorem about Vietoris maps from different approaches.
Twórcy
autor
  • Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, Republic of China
  • Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, Republic of China
Bibliografia
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  • [17] L.J. Lin and Z.T. Yu, Fixed points theorems of KKM-type maps, Nonlinear Anal. 38 (1999), 265-275.
  • [18] W.S. Massey, Singular Homology Theory, Springer-Verlag, New York 1980.
  • [19] H. Nikaidô, Coincidence and some systems of inequalities, J. Math. Soc. Japan 11 (1959), 354-373.
  • [20] S. Park, Coincidences of composites of admissible u.s.c. maps and applications, C.R. Math. Acad. Sci. Canada 15 (1993), 125-130.
  • [21] S. Park, Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps, J. Korean Math. Soc. 31 (1994), 493-519.
  • [22] X. Wu and S. Shen, A futher generalization of Yannelis-Prabhakar's continuous selection theorem and its applications, J. Math. Anal. Appl. 197 (1996), 61-74.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1033
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