Let $f(x)$ be a function of bounded variation on $[-1,1]$ and $S_n (f; x)$ the $n$th partial sum of the expansion of $f(x)$ in a Chebyshev series of the second kind. In this note we give the estimate for the rate of convergence of the sequence $S_n (f; x)$ to $f(x)$ in terms of the modulus of continuity of the total variation of $f(x)$.

In this paper we investigate the existence of mild solutions on the semi-infinite interval to second order initial value problems for a class of integrodifferential inclusions in Banach spaces. We shall make use of a theorem of Ma, which is an extension to multivalued maps on locally convex topological spaces of Schaefer's Theorem.

The minimal rank of the matrix expression $A - BX - YC$ with respect to the choice of $X$ and $Y$ are determined using generalized inverses of matrices. Some of their applications are also presented.

In this paper we examine the linear elliptic partial differential operators that appear as Euler-Lagrange systems of certain variational integrals. We give a sufficient condition for those systems to be deformable to the Laplace system.

All rings are commutative rings with identity and $J(R)$ denotes the Jacobson radical of a ring $R$. A ring $R$ is called a $SB$-ring provided that for any sequence $a_1, a_2, \ldots , a_s, a_{s+1}$ of elements in $R$ with $s \ge 2$ and $(a_1, a_2, \ldots , a_{s-1} ) \not\subseteq J(R)$, there exists $b \in R$ such that $(a_1, a_2, \ldots a_s, a_{s+1}) = (a_1, a_2, \ldots , a_s + ba_{s+1})$. By applying some of the properties of $SB$-rings, it is shown that $R[X]$ is not a Prüfer domain for any Noetherian domain $R$ which is not a field.