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W. Aziz, J. A. Guerrero and N. Merentes, “On Nemytskii Operator in the Space of Set-Valued Functions of Bounded p-Variation in the Sense of Riesz with Respect to the Weight Function,” Fasciculi Mathematici, Vol. 50, 2013, in press.

has been cited by the following article:

• TITLE: Nemytskii Operator in the Space of Set-Valued Functions of Bounded φ-Variation

  AUTHORS: Wadie Aziz

  KEYWORDS: Bounded Variation; Function of Bounded Variation in the Sense of Riesz; Variation Space; Weight Function; Banach Space; Algebra Space

  JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.6, August 29, 2013

  ABSTRACT: In 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.