Nemytskii Operator in the Space of Set-Valued Functions of Bounded <i>φ</i>-Variation

• 作者: Wadie Aziz
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: BOUNDED VARIATION FUNCTION of BOUNDED VARIATION in the Sense of Riesz VARIATION SPACE Weight FUNCTION Banach SPACE Algebra SPACE
• 年，卷（期）: 2013,（6）
• 页码范围: 563-575
• 页数: 13页
• 分类号: O1

摘要

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.