It is proved that under some conditions the set of solutions to initial value problem for second order functional differential system on an unbounded interval is a compact -set and hence nonvoid, compact and connected set in a Fréchet space. The proof is based on a Kubáček’s theorem.
M. Radulescu proved the following result: Let be a compact Hausdorff topological space and a supra-additive and supra-multiplicative operator. Then is linear and multiplicative. We generalize this result to arbitrary topological spaces.
We observe the existence of a -compact, separable topological group and a countable topological group such that the tightness of is countable, but the tightness of is equal to .
We consider some variational principles in the spaces C*(X) of bounded continuous functions on metrizable spaces X, introduced by M. M. Choban, P. S. Kenderov and J. P. Revalski. In particular we give an answer (consistent with ZFC) to a question stated by these authors.
In this paper, we present a representation theorem for probabilistic metric spaces in general.
In this paper, the α waybelow relation, which is determined by O2-convergence, is characterized by the order on a poset, and a sufficient and necessary condition for O2-convergence to be topological is obtained.
We study best approximation in -normed spaces via a general common fixed point principle. Our results unify and extend some known results of Carbone [ca:pt], Dotson [do:bs], Jungck and Sessa [ju:at], Singh [si:at] and many of others.