Conjecture [Schauder] For every non-empty convex subset C of a topological vector space E, a compact continuous mapping f : C → C has a fixed point, i.e., a point x∗ ∈ C such that f(x∗) = x∗. (See [16], problem 54). We recall that a mapping f : C → C is said to be compact if f(C) is contained in a compact subset of C. Schauder proved in 1930 that his conjecture holds for normed vector spaces an...

This paper investigates set-valued differential equations with fractional-like Hukuhara derivatives. Firstly, a novel comparison principle is given by introducing the upper quasi-monotone increasing functions. Then, stability criteria of Lipschitz and practical such different initial time are obtained via new vector Lyapunov

Finite difference kind of schemes are popular in approximating wave propagation problems finite dimensional spaces. While Yee’s original paper on the method is already from sixties, mathematically there still remains questions which not yet satisfactorily covered. In this paper, we address two issues kind. Firstly, literature scheme constructed separately for each particular type problem. Here,...