Theorems on the representation of nonlinear mapping families and implicit function theorems

We derive a result on local representations of a nonlinear mapping family in a neighborhood of a 2-regular singularity. Theorems of this kind are special forms of implicit function theorems and contain many very important results of local nonlinear analysis. Translated fromMatematicheskie Zametki, Vol. 67, No. 1, pp. 57–68, January, 2000.