We essentially extend and improve the classical result of G. H. Hardy J. E. Littlewood on strong summability Fourier series. will present an estimation generalized mean (H, Φ) as approximation version Totik type generaliza- tion Hardy, Littlewood, in case integrable functions from LΨ. As a measure such we use function constructed by Ψ com- plementary to Φ base definition LΨ points. Some corolla...

The goal of this poster is to draw attention to observational calculi, to explain their main features and to outline possibilities of their application in Semantic Web. Observational calculi were defined in the book [1] as a tool to answer the questions (i) Can computers formulate and verify scientific hypotheses? (ii) Can computers in a rational way analyze empirical data and produce a reasona...

Let φ : Mn → B(H) be an injective, completely positive contraction with ‖φ−1 : φ(Mn) → Mn‖cb ≤ 1 + δ(ǫ). We show that if either (i) φ(Mn) is faithful modulo the compact operators or (ii) φ(Mn) approximately contains a rank 1 projection, then there is a complete order embedding ψ : Mn → B(H) with ‖φ − ψ‖cb < ǫ. We also give examples showing that such a perturbation does not exist in general. As ...

Abstract In this paper, using the notion of w -distance in metric spaces, we introduce two types nonlinear contractions, $(\iota ,\psi ,\varphi ,\phi ,p)$ ( ι , ψ φ ϕ p ) and rational- , \var...

In this paper we study the generalized Fucik type eigenvalue for the boundary value problem of one dimensional p−Laplace type differential equations { −(φ(u′))′ = ψ(u), −T < x < T ; u(−T ) = 0, u(T ) = 0 (∗) where φ(s) = αs + − βs − , ψ(s) = λs + − μs − , p > 1. We obtain a explicit characterization of Fucik spectrum (α, β, λ, μ), i.e., for which the (*) has a nontrivial solution. (1991) AMS Su...

which, for invertible φ can also be expressed as, EX ≤ φ−1(E φ(X)) The term φ−1 ( E φ(X) ) can be seen as a generalized mean value [2],[1, ch.3]. The Lp norms (E|X|p)1/p for example fit this framework. The notion of convexity was generalized by B. Jessen in [2] to compare two functions in terms of the means defined by them. An increasing function φ is defined to be convex with respect to anothe...

We extend some classical results of Cowling and Meda to the noncommutative setting. Let (Tt)t>0 be a symmetric contraction semigroup on a noncommutative space Lp(M), and let the functions φ and ψ be regularly related. We prove that the semigroup (Tt)t>0 is φ-ultracontractive, i.e. ‖Ttx‖∞ ≤ Cφ(t)‖x‖1 for all x ∈ L1(M) and t > 0 if and only if its infinitesimal generator L has the Sobolev embeddi...

Given the irredundant CNF representation φ of a monotone Boolean function f : {0, 1} 7→ {0, 1}, the dualization problem calls for finding the corresponding unique irredundant DNF representation ψ of f . The (generalized) multiplication method works by repeatedly dividing the clauses of φ into (not necessarily disjoint) groups, multiplying-out the clauses in each group, and then reducing the res...