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

• Autorzy: Aziz W. , Guerrero J. A. , Merentes N.
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider the Nemytskii operator (Hf) (t) = h(t, f (t)), generated by a given set-valued function h is considered. It is shown that if H is globally Lipschitzian and maps the space of functions of bounded p-variation (with respect to a weight function α) into the space of set-valued functions of bounded q-variation (with respect to α) ) 1 < q < p, then H is of the form (Hϕ)(t) = A(t)ϕ(t) + B(t). On the other hand, if 1 < p < q, then H is constant. It generalizes many earlier results of this type due to Chistyakov, Matkowski, Merentes-Nikodem, Merentes-Rivas, Smajdor-Smajdor and Zawadzka.

Słowa kluczowe

EN

variation in the sense of Riesz set-valued functions; weight function; composition operator; Jensen equation

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2013
• Tom: Nr 50
• Strony: 17--32
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Aziz W.

• Universidad de los Andes Departamento de Física y Matemáticas Trujillo-Venezuela

autor

Guerrero J. A.

• Universidad Nacional Experimental del Táchira Dpto. de Matemática y Física San Cristábal-Venezuela

autor

Merentes N.

• Universidad Central de Venezuela Escuela de Matemáticas Caracas-Venezuela

Bibliografia

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• [8] Merentes N., Rivas S., On Nemytskij operator in the space of set-valued functions of bounded p-variation in the sense of Riesz, Public. Math. Debr., 47(1-2)(1995), 15-27.
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