Continuity of L-p Balls and an Application to Input-Output Systems

HÜSEYİN A., HÜSEYİN N., Guseinov K. G.

MATHEMATICAL NOTES, cilt.111, sa.1-2, ss.58-70, 2022 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 111 Sayı: 1-2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1134/s0001434622010072
  • Dergi Adı: MATHEMATICAL NOTES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.58-70
  • Anahtar Kelimeler: continuity, Hausdorff distance, set-valued map, input-output system, integrable output
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

In this paper, the continuity of the set-valued map p -> B-Omega,B- X,(p)(r), p is an element of (1,+infinity), is proved where B-Omega,B- X,(p)(r) is the closed ball of radius r in the space L-p(Omega, Sigma, mu; X) centered at the origin, (Omega, Sigma, mu) is a finite and positive measure space, and X is a separable Banach space. An application to input-output systems described by Urysohn type integral operators is discussed.