A real number x is f-bounded computable (f-bc, for short) for a function f if there is a computable sequence (xs) of rational numbers which converges to x f-bounded effectively in the sense that, for any natural number n, the sequence (xs) has at most f (n) non-overlapping jumps of size larger than 2−n. f-bc reals are called divergence bounded computable if f is computable. In this paper we giv...

If T = {T (t); t ≥ 0} is a strongly continuous family of bounded linear operators between two Banach spaces X and Y and f ∈ L1(0, b, X), the convolution of T with f is defined by (T ∗f)(t) = ∫ t 0 T (s)f(t− s)ds. It is shown that T ∗ f is continuously differentiable for all f ∈ C(0, b, X) if and only if T is of bounded semi-variation on [0, b]. Further T ∗ f is continuously differentiable for a...

We establish Liouville-type theorems for stable and finite Morse index weak solutions of −∆pu = f(x)F (u) in R . For a general non-linearity F ∈ C(R) and f(x) = |x|, we prove such theorems in dimensions N ≤ 4(p+α) p−1 +p, for bounded radial stable solutions. Then, we give some point-wise estimates for not necessarily bounded solutions. Also, similar theorems will be proved for both radial finit...

We prove that every set system of bounded VC-dimension has a fractional Helly property. More precisely, if the dual shatter function of a set system F is bounded by o(m k), then F has fractional Helly number k. This means that for every > 0 there exists a > 0 such that if F 1 ; F 2 ; : : : ; F n 2 F are sets with T i2I F i 6 = ; for at least ? n k sets I f1; 2; : : :; ng of size k, then there e...

The purpose of this paper is to characterize the Banach spaces and the locally convex spaces E for which bounded additive measures or bounded σadditive measures with values in L(E, F ), the space of continuous linear maps from E into F , are of bounded semi-variation for any Banach space or locally convex space F . This paper gives an answer to a problem posed by D.H. Tucker in [6].

let $t$ be a bounded operator on the banach space $x$ and $ph$ be an analytic self-map of the unit disk $bbb{d}$‎. ‎we investigate some operator theoretic properties of‎ ‎bilateral composition operator $c_{ph‎, ‎t}‎: ‎f ri t circ f circ ph$ on the vector-valued hardy space $h^p(x)$ for $1 leq p leq‎ ‎+infty$.‎ ‎compactness and weak compactness of $c_{ph‎, ‎t}$ on $h^p(x)$‎ ‎are characterized an...

in this paper, we investigate the existence of positive solutions for the ellipticequation $delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $omega$ of $r^{n}$, $ngeq2$, with navier boundary conditions. we show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...

Let σ, τ : N→N be two sequences of natural numbers. We say that σ dominates τ if σ(n) τ(n) for every n greater than some n0 ∈ N. Now let G be an infinite graph, and assume the vertices of G are labelled with natural numbers, say by f : V (G)→N. Then each ray (one-way infinite path) R = x0x1 . . . in G gives rise to a sequence τR := (f(x0), f(x1), . . .); we say that σ dominates R if σ dominates...