Abstract
Suppose thatF:D⊂R n×Rm→Rn, withF(x 0,y 0)=0. The classical implicit function theorem requires thatF is differentiable with respect tox and moreover that ∂1 F(x 0,y 0) is nonsingular. We strengthen this theorem by removing the nonsingularity and differentiability requirements and by replacing them with a one-to-one condition onF as a function ofx.
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Ortega, J. M., andRheinboldt, W. C.,Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, New York, 1970.
Greenberg, M.,Lectures on Algebraic Topology, W. A. Benjamin, Menlo Park, California, 1971.
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Communicated by G. Leitmann
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Jittorntrum, K. An implicit function theorem. J Optim Theory Appl 25, 575–577 (1978). https://doi.org/10.1007/BF00933522
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DOI: https://doi.org/10.1007/BF00933522