Abstract
Let K be a closed convex cone with nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. If {F t : t ≥ 0} is a regular cosine family of continuous additive set-valued functions F t : K → cc(K) such that x ∈ F t (x) for t ≥ 0 and x ∈ K, then
.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aghajani M., Nourouzi K., On the regular cosine family of linear correspondences, Aequationes Math. 83 (2012), 215–221
Edgar G.A., Measure, Topology and Fractal Geometry, Undergrad.Texts Math., Springer-Verlag New York Inc., New York, 1990
Łojasiewicz S., An Introduction to the Theory of Real Functions, Wiley, Chichester — New York — Brisbane — Toronto — Singapore 1988
Mainka-Niemczyk E., Integral representation of set-valued sine families, J. Appl. Anal. 18(2) (2012), 243–258
Mainka-Niemczyk E., Multivalued second order differential problem, Ann. Univ. Paedagog. Crac. Stud. Math. 11 (2012), 53–67
Mainka-Niemczyk E., Some properties of set-valued sine families, Opuscula Math. 32(1) (2012), 157–168
Nikodem K., On concave and midpoint concave set-valued functions, Glasnik Mat. 22(42)(1987), 69–76
Piszczek M., Integral representations of convex and concave set-valued functions, Demonstratio Math. 35 (2002), 727–742
Piszczek M., Second Hukuhara derivative and cosine family of linear set-valued functions, Ann. Acad. Peadagog. Crac. Stud. Math. 5 (2006), 87–98
Piszczek M., On multivalued cosine families, J. Appl. Anal. 14 (2007), 57–76
Piszczek M., On multivalued iteration semigroups, Aequationes Math. 81 (2011), 97–108
Sova M., Cosine operator functions, Dissertationes Math. (Rozprawy Mat.) 49 (1966), 1–47
Smajdor A., Iteration of multivalued functions, Prace Naukowe Uniwersytetu Slaskiego w Katowicach Nr 759, Uniwersytet Slaski w Katowicach 1985
Smajdor A., On regular multivalued cosine families, Ann. Math. Sil. 13 (1999), 271–280
Smajdor A., Hukuhara’s derivative and concave iteration semigrups of linear set-valued functions, J. Appl. Anal. 8 (2002), 297–305
Smajdor A., Hukuhara’s differentiable iteration semigrups of linear set-valued functions, Ann. Polon. Math. 83(1) (2004), 1–10
Trevis C.C., Webb G.F., Cosine families and abstract nonlinear second order differential equations, Acta Math. Acad. Sci. Hungar. 32(3–4) (1978), 75–96
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Smajdor, A., Smajdor, W. Commutativity of set-valued cosine families. centr.eur.j.math. 12, 1871–1881 (2014). https://doi.org/10.2478/s11533-014-0433-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.2478/s11533-014-0433-y