Proceedings Mathematical Sciences
In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.
In this article, we give conditions under which we can compute the conjugate of a convex function on the product of two Fréchet spaces defined in terms of another convex function on the product of two (possibly different) Fréchet spaces. We use this result to give simple proofs of some (both old and new) results for Banach spaces, and deduce some (...
Lobachevskii Journal of Mathematics
We consider linear normed spaces of measurable functions dominated by positive measurable function powered by real positive parameter. Also, we consider its dual and predual, and we propose a method for constructing a limit spaces of these functional spaces taken by power parameter. We prove that these limit spaces are (LF)-spaces and also prove th...