Here in this paper we intend to deal with two questions: How large is a “Lebesgue Class” in the topology of Lebesgue integrable functions, and also what can be said regarding the topological size of a “Lebesgue set” in R?, ...

In this paper, the Hyers-Ulam stability of the Volterra integrodifferential equation and the Volterra equation on the finite interval [0, T], T > 0, are studied, where the state x(t) take values in a Banach space X.

A simple age-dependent population dynamics model with an additional structure or physiological variable is presented in its variational formulation. Although the model is well-posed, the closed form solution with space ...

We prove in this paper that any maximal, with respect to inclusion, subset of N – the family of all increasing sequences of positive integers – possessing the harmonic series property has the cardinality of the ...