Suppose that F:D⊂Rn×Rm→Rn, with F(x0, y0)=0. The classical implicit function theorem requires that F is differentiable with respect to x and moreover that ∂1F(x0, y0) is nonsingular. We strengthen this theorem by removing the nonsingularity and differentiability requirements and by replacing them with a one-to-one condition on F as a function of x. © 1978 Plenum Publishing Corporation.
CITATION STYLE
Jittorntrum, K. (1978). An implicit function theorem. Journal of Optimization Theory and Applications, 25(4), 575–577. https://doi.org/10.1007/BF00933522
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