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 the proof, the local one-to-one condition forF(·,y):A ⊂Rn →Rn for ally ∈B is consciously or unconsciously treated as implying thatF(·,y) mapsA one-to-one ontoF(A, y) for ally ∈B, and the proof is not perfect. A proof can be given directly, and the theorem is shown to be the strongest, in the sense that the condition is truly if and only if.
Key WordsImplicit function theorem nonlinear network analysis computer-aided design
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