Abstract
Abstract
Let K be a closed convex cone in a real Banach space,
{H\colon K\to\operatorname{cc}(K)}
a continuous sublinear correspondence with nonempty, convex and compact values in K, and let
{f\colon\mathbb{R}\to\mathbb{R}}
be defined by
{f(t)=\sum_{n=0}^{\infty}a_{n}t^{n}}
, where
{t\in\mathbb{R}}
,
{a_{n}\geq 0}
,
{n\in\mathbb{N}}
.
We show that the correspondence
{F^{t}(x)\mathrel{\mathop{:}}=\sum_{n=0}^{\infty}a_{n}t^{n}H^{n}(x),(x\in K)}
is continuous and sublinear for every
{t\geq 0}
and
{F^{t}\circ F^{s}(x)\subseteq\sum_{n=0}^{\infty}c_{n}H^{n}(x)}
,
{x\in K}
,
where
{c_{n}=\sum_{k=0}^{n}a_{k}a_{n-k}t^{k}s^{n-k}}
,
{t,s\geq 0}
.
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Mathematical Physics
Reference14 articles.
1. An embedding theorem for space of convex sets;Proc. Amer. Math. Soc.,1952
2. On some families of set-valued functions;Aequationes Math.,2009
3. Increasing iteration semigroups of Jensen set-valued functions;Aequationes Math.,1998
4. On a family of set-valued functions;Publ. Math. Debrecen,1995
5. On a family of set-valued functions;Publ. Math. Debrecen,1995