UNIFORMLY BOUNDED COMPOSITION OPERATORS

We prove that if a uniformly bounded (or equidistantly uniformly bounded) Nemytskij operator maps the space of functions of bounded ${\it\varphi}$-variation with weight function in the sense of Riesz into another space of that type (with the same weight function) and its generator is continuous with respect to the second variable, then this generator is affine in the function variable (traditionally, in the second variable).

On Nemytskij operator of substitution in the C1 space of set-valued functions

We consider the Nemytskij operator, i.e., the operator of substitution, defined by (

On the Continuity of the Nemytskij Operator between the Spaces 𝐿𝑝1(𝑋) and 𝐿𝑝2(𝑋)

We provide a generalized sufficient condition for the continuity of the Nemytskij operator between 𝐿𝑝1(𝑋) and 𝐿𝑝2(𝑋). An example is given.