http://hdl.handle.net/11716/5434 2026-04-19T11:30:02Z http://hdl.handle.net/11716/6649 10th International Conference on Functional Equations and Inequalities, Będlewo, September 11-17, 2005 Choczewski, Bogdan 2006-01-01T00:00:00Z http://hdl.handle.net/11716/6648 9th International Conference on Functional Equations and Inequalities, Złockie, September 7-13, 2003 Choczewski, Bogdan 2006-01-01T00:00:00Z http://hdl.handle.net/11716/6647 Second Hukuhara derivative and cosine family of linear set-valued functions Piszczek, Magdalena Let $K$ be a closed convex cone with the 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 linear set-valued functions $F_t:K → cc(K), x ∈ F_t(x)$ for $t ≥ 0, x ∈ K$ and $F_t ᴑ F_s = F_s ᴑ F_t$ for $s; t ≥ 0$, then \[D^2F_t(x) = F_t(H(x))\] for $x ∈ K$ and $t ≥ 0$, where $D^2F_t(x)$ denotes the second Hukuhara derivative of $F_t(x)$ with respect to $t$ and $H(x)$ is the second Hukuhara derivative of this multifunction at $t = 0$. 2006-01-01T00:00:00Z http://hdl.handle.net/11716/6646 Some properties of convex and *-concave multifunctions Piątek, Bożena We investigate some properties of *-concave and convex multifunctions on the real line with convex bounded closed values. In particularly we consider the Hadamard inequality and the Hardy-Littlewood-Pólya majorization theory in the case of multifunctions. 2006-01-01T00:00:00Z