Uniformly bounded composition operators between general Lipschitz function normed spaces

Abstract

The notions of uniform boundedness and equidistant uniform boundedness of an
operator (both weaker then usual boundedness) are introduced. The main
results say that the generator of any uniformly bounded (or equidistantly
uniformly bounded) composition Nemytskiĭ operator acting between general
Lipschitzian normed function spaces must be affine with respect to the
function variable.