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 | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-1989-0993760-8

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