banach contraction principle has been generalized in different spaces by mathematicians over the years. mustafa and sims [18] proposed a new class of generalized metric spaces, which are called as g-metric spaces. in this type of spaces a non-negative real number is assigned to every triplet of elements. many mathematicians studied extensively various results on g-metric spaces by using the con...

In this paper, we try to study a special class of frame wavelets in Banach spaces whose Fourier transforms are supported by frame wavelet sets. Our results generalize the various results of [2] to Banach spaces other than Hilbert spaces using the Feichtinger and Gröchenig theory. 2001 AMS Subject Classification : 42C99

where here, and in what follows, Eε denotes the expectation with respect to uniformly chosen ε = (ε1, . . . , εn) ∈ {−1, 1}. The infimum over all constants T for which (1.1) holds is denoted by Tp(X). An important theorem of Ribe [12] states that Banach spaces which are uniformly homeomorphic must have the same isomorphic local properties. In other words, any property which remains valid under ...

We present two examples of nice normal spaces X having the property that for some xed-point free homeomorphism on X its Cech-Stone extension has a xed point. One of the spaces presented here is locally countable, locally compact, separable , normal, countably paracompact and weakly zero-dimensional. The other one is hereditarily normal and strongly zero-dimensional. Our construction of this exa...

Abstract. Here a new condition for the geometry of Banach spaces is introduced and the operator–valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and Hörmander-Mikhlin conditions are established. As an application of main results the regularity properties of degenerate elliptic differential operator equation...

Previous examples of non-type (D) maximal monotone operators were restricted to 1, L1, and Banach spaces containing isometric copies of these spaces. This fact led to the conjecture that non-type (D) operators were restricted to this class of Banach spaces. We present a linear non-type (D) operator in c0.

The goal of this paper is to investigate the advantages and disadvantages of learning in Banach spaces over Hilbert spaces. While many works have been carried out in generalizing Hilbert methods to Banach spaces, in this paper, we consider the simple problem of learning a Parzen window classifier in a reproducing kernel Banach space (RKBS)—which is closely related to the notion of embedding pro...

In this paper, we solve the additive ρ-functional inequalities ‖f(x+ y)− f(x)− f(y)‖ ≤ ∥∥∥∥ρ(2f (x+ y 2 ) − f(x)− f(y) )∥∥∥∥ , (1) ∥∥∥∥2f (x+ y 2 ) − f(x)− f(y) ∥∥∥∥ ≤ ‖ρ (f(x+ y)− f(x)− f(y))‖ , (2) where ρ is a fixed non-Archimedean number with |ρ| < 1 or ρ is a fixed complex number with |ρ| < 1. Using the direct method, we prove the Hyers-Ulam stability of the additive ρ-functional inequalit...

Our aim is to give a characterization of the BMO norm via Banach function spaces based on the Rubio de Francia algorithm. Our proof is different from the one by Ho [Atomic decomposition of Hardy spaces and characterization of BMO via Banach function spaces, Anal. Math. 38 (2012), 173–185].

We lift upper and lower estimates from linear functionals to n-homogeneous polynomials and using this result show that l ∞ is finitely represented in the space of n-homogeneous poly-nomials, n ≥ 2, for any infinite dimensional Banach space. Refinements are also given. The classical Dvoretsky spherical sections theorem [5,13] states that l 2 is finitely represented in any infinite dimensional Ba...