The theory of weighted inequalities for the Hardy operator, acting on monotone functions in R+, was first introduced in [2]. Extensions of these results to higher dimension have been considered only in very specific cases. In particular, in the diagonal case, only for p = 1 (see [5]). The main difficulty in this context is that the level sets of the monotone functions are not totally ordered, c...

The functions m := j j 2m d if d is odd, and m := j j 2m d log j j if d is even, are known as surface splines, and are commonly used in the interpolation or approximation of smooth functions. We show that if one's domain is the unit ball in R, then the approximation order of the translates of m is at most m. This is in contrast to the case when the domain is all of R where it is known that the ...

Abstract We present two theoretical results and surprising conjectures concerning convergence properties of Broyden’s method for smooth nonlinear systems equations. First, we show that when is applied to a mapping $$F:\mathbb {R}^n\rightarrow \mathbb {R}^n$$ F : R <...

In this paper, we define the space Sαθ (∆mv, f) of all f)-lacunary statistical convergent sequences order α with help unbounded modulus function f, lacunary sequence (θ), generalized difference operator ∆ mv and real number ∈ (0, 1]. We also introduce ωαθ strong summable α. Properties related to these spaces are studied. Inclusion relations between ωα θ established under certain conditions.