An implicit function theorem

  title={An implicit function theorem},
  author={Krisorn Jittorntrum},
  journal={Journal of Optimization Theory and Applications},
  • K. Jittorntrum
  • Published 1 August 1978
  • Mathematics
  • Journal of Optimization Theory and Applications
Suppose thatF:D⊂Rn×Rm→Rn, withF(x0,y0)=0. The classical implicit function theorem requires thatF is differentiable with respect tox 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 onF as a function ofx. 
An implicit function theorem: Comment
In Ref. 1, Jittorntrum proposed an implicit function theorem for a continuous mappingF:Rn ×Rm →Rn, withF(x0,y0)=0, that requires neither differentiability ofF nor nonsingularity of ∂xF(x0,y0). In theExpand
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