In this paper we investigate weakly continuous solutions of some integral equations in Banach spaces. Moreover, we prove a fixed point theorem which is very useful in our considerations.
We prove that a set of weak solutions of the nonlinear Volterra integral equation has the Kneser property. The main condition in our result is formulated in terms of axiomatic measures of weak noncompactness.
In this note we investigate a relationship between the boundary behavior of power series and the composition of formal power series. In particular, we prove that the composition domain of a formal power series is convex and balanced which implies that the subset consisting of formal power series which can be composed by a formal power series possesses such properties. We also provide a necessary and sufficient condition for the superposition operator to map into itself or to map into...
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