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In this paper we prove the existence of solutions of the differential inclusions

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\left\{ \begin{gathered} \dot X(t) \in - A_t (X(t)) + F(t,X(t)),,0 \leqslant t \leqslant T_0 \hfill \\ X(0) = x_0 \hfill \\ \end{gathered} \right.$$ \end{document}
whereA t is a multivaluedm-accretive operator on a Banach spaceE andF is a measurable multifunction defined on the set , lower semicontinuous inx and its values are not necessarily convex inE. This result generalizes some results in [1] and [9].

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] Fu , K. A. Zhang , L. X. 2009 A general LIL for trimmed sums of random fields in Banach spaces Acta Math. Hungar. 122 91 – 103 10.1007/s

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Abstract  

We show that, in the classes of functions with values in a real or complex Banach space, the problem of Hyers-Ulam stability of a linear functional equation of higher order (with constant coefficients) can be reduced to the problem of stability of a first order linear functional equation. As a consequence we prove that (under some weak additional assumptions) the linear equation of higher order, with constant coefficients, is stable in the case where its characteristic equation has no complex roots of module one. We also derive some results concerning solutions of the equation.

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In this paper we prove the following result. Let X be a real or complex Banach space, let L ( X ) be the algebra of all bounded linear operators on X , and let A ( X ) ⊂ L ( X ) be a standard operator algebra. Suppose we have a linear mapping D : A ( X ) → L ( X ) satisfying the relation D ( A 3 ) = D ( A ) A 2 + AD ( A ) A + A 2 D ( A ), for all AA ( X ). In this case D is of the form D ( A ) = ABBA , for all AA ( X ) and some BL ( X ). We apply this result, which generalizes a classical result of Chernoff, to semisimple H *-algebras.

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, New York , 1977 . [3] Campbell , S. L. and Faulkner , G. D. , Operators on Banach spaces with complemented ranges , Acta Math. Acad

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