A nonlinear variation of constants method for integro differential and integral equations

A Class of Operator Inequalities on Ordered Linear Spaces

“…Suppose that (2.1') T^ is monotcne, for all i = 1,...,n, n (2.2') 2 T. is a normal mapping. i=1 1 -147 - It is important to observe that, in the reasonings involved in the proofs of the above theorems, the multiplication by scalars was not effectively used. This leads us to the conclusion that these results might be formulated in a more general setting, by replacing the ordered linear space X by an ordered set (X, s), endowed with an internal associative opera-2 tion + :X -^X, compatible, in a certain sense, with the ordering (i.e., (a) the internal operation "+" is a monotone mapping from X to X, (b) x<x+y, for every x,yeX).…”

On the stability of volterra integral equations with seperable kernels

“…In this paper we mainly concentrate on the qualitative behaviour of the solutions of the scalar equation with seperable kernels, also known as Pincherle-Goursat (P-G) kernels By employing comparison type and preservation type results [3][4][5][6]9], the domain of applicability of such analysis can be extended to cover a wider class of integral equations.…”