Some families of sublinear correspondences

• Autorzy: Najmadi Parvaneh , Aghajani Masoumeh

Identyfikatory

DOI

10.1515/jaa-2019-0010

• Języki publikacji: EN

Abstrakty

EN

Let K be a closed convex cone in a real Banach space, H: K → cc(K) a continuous sublinear correspondence with nonempty, convex and compact values in K, and let f : ℝ → ℝ be defined by f(t) = Σ^∞_{n =0} a_ntⁿ, where t ∈ ℝ, a_n ≥ 0, n ∈ ℕ.We show that the correspondence F^t(x) := Σ^∞_{n =0} a_n tⁿHⁿ(x), (x ∈ K) is continuous and sublinear for every t ≥ 0 and F^t ∘ F^s(x) ⊆ Σ^∞_n=0 c_nHⁿ(x), x ∈ K, where c_n = Σ>sup>n_{k = 0} a_ka_n−k t^ks^n−k, t, s ≥ 0.

Słowa kluczowe

EN

sublinear correspondence; Hausdorff metric; iteration

PL

odpowiedniość podliniowa; metryka Hausdorffa; iteracja

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2019
• Tom: Vol. 25, nr 1
• Strony: 91--95
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Najmadi Parvaneh

• Department of Mathematics, Faculty of Science, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran

autor

Aghajani Masoumeh

• Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, P.O. Box 16785-136, Tehran, Iran

Bibliografia

• [1] M. Aghajani, K. Nourouzi and D. O’Regan, The continuity of linear and sublinear correspondences defined on cones, Bull. Iranian Math. Soc. 41 (2015), no. 1, 43-55.
• [2] C. D. Aliprantis and K. C. Border, Infinite Dimensional Analysis: A Hitchhiker’s Guide, 3rd ed., Springer, Berlin, 2006.
• [3] M. Piszczek, On multivalued cosine families, J. Appl. Anal. 13 (2007), no. 1, 57-76.
• [4] J. Plewnia, On a family of set-valued functions, Publ. Math. Debrecen 46 (1995), no. 1-2, 149-159.
• [5] H. Rädström, An embedding theorem for space of convex sets, Proc. Amer. Math. Soc. 3 (1952), 165-169.
• [6] A. Smajdor, Increasing iteration semigroups of Jensen set-valued functions, Aequationes Math. 56 (1998), no. 1-2, 131-142.
• [7] J. Szczawińska, On some families of set-valued functions, Aequationes Math. 78 (2009), no. 1-2, 157-166.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).