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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A short proof and a generalization of Miranda's existence theorem


Author: Michael N. Vrahatis
Journal: Proc. Amer. Math. Soc. 107 (1989), 701-703
MSC: Primary 54H25; Secondary 47H10, 55M20, 58C30, 65H10
MathSciNet review: 993760
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Abstract: Miranda gave in [5] an equivalent formulation of the famous Brouwer fixed point theorem. We give a short proof of Miranda's existence theorem and then using the results obtained in this proof we give a generalization of a well-known variant of Bolzano's existence theorem. Finally, we give a generalization of Miranda's theorem.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0993760-8
PII: S 0002-9939(1989)0993760-8
Keywords: Fixed points, Brouwer fixed point theorem, Miranda existence theorem, Bolzano existence theorem, systems of nonlinear algebraic or transcendental equations
Article copyright: © Copyright 1989 American Mathematical Society