On the continuity properties of the L_p balls

• Autorzy: Huseyin Nesir , Huseyin Anar

Identyfikatory

DOI

10.1515/jaa-2022-1008

• Języki publikacji: EN

Abstrakty

EN

In this paper the right upper semicontinuity at p = 1 and continuity at p = ∞ of the set-valued map p → B_Ω,X,p(r), p ∈ [1, ∞], are studied where B_Ω,X,p(r) is the closed ball of the space L_p(Ω, Σ, μ;X) centered at the origin with radius r, (Ω, Σ, μ) is a finite and positive measure space, X is a separable Banach space. It is proved that the considered set-valued map is right upper semicontinuous at p = 1 and continuous at p = ∞. An application of the obtained results to the set of integrable outputs of the input-output system described by the Urysohn-type integral operator is discussed.

Słowa kluczowe

EN

continuity; semicontinuity; set-valued map; Urysohn integral operator; input-output system

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2023
• Tom: Vol. 29, nr 1
• Strony: 151--159
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Huseyin Nesir

• Department of Mathematics and Science Education, Sivas Cumhuriyet University, Sivas, Türkiye

• https://orcid.org/0000-0001-7652-1505

autor

Huseyin Anar

• Department of Mathematics and Science Education, Sivas Cumhuriyet University, Sivas, Türkiye

• https://orcid.org/0000-0002-3911-2304

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).