In the present paper we establish an abstract principle of condensation of singularities for families consisting of set-valued mappings. By using it as a basic tool, the condensation of the singularities and the equicontinuity of certain families of generalized convex set-valued mappings are studied. In particular, a principle of condensation of the singularities of families of closed convex pr...

A Liapunov theorem is introduced guaranteeing uniform boundedness and uniform ultimate boundedness for a timevarying nonlinear system _ x(t) = f(x(t); t). The study of uniform boundedness and uniform ultimate boundedness of particular classes of time-varying nonlinear systems _ x(t) = f(x(t); t) is reduced to the study of the corresponding timeinvariant frozen systems _ x(t) = f(x(t); ) for all...

The concept of b-linear functional and its different types continuity in linear n-normed space are presented some their properties being established. We derive the Uniform Boundedness Principle Hahn-Banach extension Theorem with help bounded functionals case spaces discuss examples applications. Finally, we present weak*convergence for sequence space.

A summability theorem of Landau, which classically is a simple consequence of the uniform boundedness theorem, is examined within Bishop-style constructive mathematics. It is shown that the original theorem is nonconstructive, and that a natural weakening of the theorem is constructively equivalent to Ishihara’s principle BD-N. The paper ends with a number of results that, while not as strong a...