Characterization of Globally Lipschitz Nemytskiĭ Operators Between Spaces of Set-Valued Functions of Bounded φ-Variation in the Sense of Riesz

• Autorzy: N. Merentes , J. L. Sánchez Hernández
• Języki publikacji: EN

Abstrakty

EN

Let (X,∥·∥) and (Y,∥·∥) be two normed spaces and K be a convex cone in X. Let CC(Y) be the family of all non-empty convex compact subsets of Y. We consider the Nemytskiĭ operators, i.e. the composition operators defined by (Nu)(t) = H(t,u(t)), where H is a given set-valued function. It is shown that if the operator N maps the space $RV_{φ₁}([a,b];K)$ into $RW_{φ₂}([a,b];CC(Y))$ (both are spaces of functions of bounded φ-variation in the sense of Riesz), and if it is globally Lipschitz, then it has to be of the form H(t,u(t)) = A(t)u(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. This generalizes results of G. Zawadzka [12], A. Smajdor and W. Smajdor [11], N. Merentes and K. Nikodem [5], and N. Merentes and S. Rivas [7].

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: 52
• Numer: 4
• Strony: 417-430

Daty

wydano

2004

Twórcy

autor

N. Merentes

• Departamento de Matemática, Universidad Central de Venezuela, Caracas 1020A, Venezuela

autor

J. L. Sánchez Hernández

• School of Mathematics, Georgia Tech, Atlanta, GA 30332-0160, U.S.A.

Identyfikatory

DOI

10.4064/ba52-4-8