On the Nemytskii operator in the space of functions of bounded (p, 2, α)-variation with respect to the weight function

• Autorzy: Aziz W.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we consider the Nemytskii operator (H f) (t) = h(t, f(t)), generated by a given function h. It is shown that if H is globally Lipschitzian and maps the space of functions of bounded (p, 2, α)-variation (with respect to a weight function α) into the space of functions of bounded (q, 2, α)-variation (with respect to α) 1 < q < p, then H is of the form (H f) (t) = A(t)f(t) + B(t). On the other hand, if 1 < p < q then H is constant. It generalize several earlier results of this type due to Matkowski–Merentes and Merentes. Also, we will prove that if a uniformly continuous Nemytskii operator maps a space of bounded variation with weight function in the sense of Merentes into another space of the same type, its generator function is an affine function.

Słowa kluczowe

EN

variation in the sense of De la Vallée Poussin; variation in the sense of Riesz; α-convex functions; weight function; composition operator; Jensen equation

PL

wariacje; funkcje α-wypukłe; waga; operator złożony; równanie Jensena

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 4
• Strony: 933--948
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Aziz W.

• Universidad de Los Andesm Departamento de Física Y Matemática, Trujillo-Venezuela

Bibliografia

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