in this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice banach spaces. also, we give some results about simultaneous approximations of normal sets.

in this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice banach spaces. also, we give some results about simultaneous approximations of normal sets.

Let P be a class of Banach spaces and let T = {Tα}α∈A be a set of metric spaces. We say that T is a set of test-spaces for P if the following two conditions are equivalent: (1) X / ∈ P; (2) The spaces {Tα}α∈A admit uniformly bilipschitz embeddings into X. The first part of the paper is devoted to a simplification of the proof of the following test-space characterization obtained in M. I. Ostrov...

in this paper, we prove the generalized hyers--ulamstability of a quadratic and quartic functional equation inintuitionistic fuzzy banach spaces.

We generalize an important class of Banach spaces, namely the M embedded Banach spaces, to the non-commutative setting of operator spaces. The one-sided M -embedded operator spaces are the operator spaces which are one-sided M -ideals in their second dual. We show that several properties from the classical setting, like the stability under taking subspaces and quotients, unique extension proper...

In this paper we present an abstract framework for construction of Banach spaces of distributions from group representations. This generalizes the theory of coorbit spaces initiated by H.G. Feichtinger and K. Gröchenig in the 1980’s. Spaces that can be described by this new technique include the whole Banach-scale of Bergman spaces on the unit disc. For these Bergman spaces we show that atomic ...

In this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in Banach spaces admitting the existence of a lower solution.