In this paper, we prove the generalized Hyers--Ulamstability of a quadratic and quartic functional equation inintuitionistic fuzzy Banach spaces.

We prove that the Banach spaces (⊕n=1`p )`q , which are isomorphic to the Besov spaces on [0, 1], have greedy bases, whenever 1 ≤ p ≤ ∞ and 1 < q < ∞. Furthermore, the Banach spaces (⊕n=1`p )`1 , with 1 < p ≤ ∞, and (⊕n=1`p )c0 , with 1 ≤ p < ∞ do not have a greedy bases. We prove as well that the space (⊕n=1`p )`q has a 1-greedy basis if and only if 1 ≤ p = q ≤ ∞.

In this article we show that a number of apparently different properties coincide on tite set of holomorpitic functions on a strict inductive limit (aH inductive limits are asgumed to be countable and proper) of Banach spaces and that they are ¿II satisfied only ‘u tite trivial case of a strict inductive limit of finite dimensional spaces. Thus tite linear properties of a strict inductive Iimit...

Motivated by multi-task machine learning with Banach spaces, we propose the notion of vectorvalued reproducing kernel Banach spaces (RKBS). Basic properties of the spaces and the associated reproducing kernels are investigated. We also present feature map constructions and several concrete examples of vector-valued RKBS. The theory is then applied to multi-task machine learning. Especially, the...

The main purposes of this paper are (1) To survey the area of coarse embeddability of metric spaces into Banach spaces, and, in particular, coarse embeddability of different Banach spaces into each other; (2) To present new results on the problems: (a) Whether coarse non-embeddability into l2 implies presence of expander-like structures? (b) To what extent l2 is the most difficult space to embe...

Several results are established about Banach spaces X which can be renormed to have the uniform Kadec-Klee property. It is proved that all such spaces have the complete continuity property. We show that the renorming property can be lifted from X to the Lebesgue-Bochner space L2(X) if and only if X is super-re exive. A basis characterization of the renorming property for dual Banach spaces is g...

In this paper, we study a class of Banach spaces, called φ-spaces. In a natural way, we associate a measure of weak compactness in such spaces and prove an analogue of Sadovskii fixed point theorem for weakly sequentially continuous maps. A counter-example is given to justify our requirement. As an application, we establish an existence result for a Hammerstein integral equation in a Banach space.

Following results of Bourgain and Gorelik we show that the spaces lp, 1 < p < ∞, as well as some related spaces have the following uniqueness property: If X is a Banach space uniformly homeomorphic to one of these spaces then it is linearly isomorphic to the same space. We also prove that if a C(K) space is uniformly homeomorphic to c0, then it is isomorphic to c0. We show also that there are B...

In this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the Bag and Samanta’s operator norm on Felbin’s-type fuzzy normed spaces. In particular, the completeness of this space is studied. By some counterexamples, it is shown that the inverse mapping theorem and the Banach-Steinhaus’s theorem, are not valid for this fuzzy setting. Also...