Wadie Aziz2026-03-222026-03-22201310.4236/apm.2013.36072https://doi.org/10.4236/apm.2013.36072https://andeanlibrary.org/handle/123456789/62645In this paper we consider the Nemytskii operator, i.e., the composition operator defined by (Nf)(t)=H(t,f(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of functions bounded φ1-variation in the sense of Riesz with respect to the weight function αinto the space of set-valued functions of bounded φ2-variation in the sense of Riesz with respect to the weight, if it is globally Lipschitzian, then it has to be of the form (Nf)(t)=A(t)f(t)+B(t), where A(t) is a linear continuous set-valued function and B is a set-valued function of bounded φ2-variation in the sense of Riesz with respect to the weight.enMathematicsBounded functionBounded operatorOperator (biology)Bounded variationFunction (biology)Space (punctuation)Set (abstract data type)Quasinormal operatorDiscrete mathematicsarticle