, Volume 25, Issue 4, pp 575-577

An implicit function theorem

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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.

Communicated by G. Leitmann