The best constant of Sobolev inequality corresponding to clamped boundary value problem.
The best lower bound depended on two fixed variables for Jensen's inequality with ordered variables.
The best possibility of the bound for the Kantorovich inequality and some remarks.
The bitransitive continuous maps of the interval are conjugate to maps extremely chaotic a. e.
The Borel structure of some non-Lebesgue sets
For a given function in some classes related to real derivatives, we examine the structure of the set of points which are not Lebesgue points. In particular, we prove that for a summable approximately continuous function, the non-Lebesgue set is a nowhere dense nullset of at most Borel class 4.
The Box Dimension of Completely Invariant Subsets for Expanding Piecewise Monotonic Transformations.
The box-counting dimension of the sine-curve
The Brascamp–Lieb inequalities: recent developments
We discuss recent progress on issues surrounding the Brascamp–Lieb inequalities.
The C k Space
In this article, we formalize continuous differentiability of realvalued functions on n-dimensional real normed linear spaces. Next, we give a definition of the Ck space according to [23].
The calculus of operator functions and operator convexity [Book]
The case of equality in Landau's problem.
The characterization of radial subspaces of Besov and Lizorkin-Triebel spaces by differences
We continue our earlier investigations of radial subspaces of Besov and Lizorkin-Triebel spaces on . This time we study characterizations of these subspaces by differences.
The Choquet integral as Lebesgue integral and related inequalities
The integral inequalities known for the Lebesgue integral are discussed in the framework of the Choquet integral. While the Jensen inequality was known to be valid for the Choquet integral without any additional constraints, this is not more true for the Cauchy, Minkowski, Hölder and other inequalities. For a fixed monotone measure, constraints on the involved functions sufficient to guarantee the validity of the discussed inequalities are given. Moreover, the comonotonicity of the considered functions...
The coarsest topology for -approximately continuous functions
The compositions of differential operations and the Gâteaux directional derivative.
The cone of nonnegative polynomials with nonnegative coefficients and linear operators preserving this cone
Let be the cone of real univariate polynomials of degree ≤ 2n which are nonnegative on the real axis and have nonnegative coefficients. We describe the extremal rays of this convex cone and the class of linear operators, acting diagonally in the standard monomial basis, preserving this cone.
The construction of some means.
The continuous solutions of a generalized Dhombres functional equation
We consider the functional equation where is a given increasing homeomorphism of an open interval and is an unknown continuous function. In a series of papers by P. Kahlig and J. Smítal it was proved that the range of any non-constant solution is an interval whose end-points are fixed under and which contains in its interior no fixed point except for . They also provide a characterization of the class of monotone solutions and prove a necessary and sufficient condition for any solution...
The converse of the Hölder inequality and its generalizations
Let (Ω,Σ,μ) be a measure space with two sets A,B ∈ Σ such that 0 < μ (A) < 1 < μ (B) < ∞ and suppose that ϕ and ψ are arbitrary bijections of [0,∞) such that ϕ(0) = ψ(0) = 0. The main result says that if for all μ-integrable nonnegative step functions x,y then ϕ and ψ must be conjugate power functions. If the measure space (Ω,Σ,μ) has one of the following properties: (a) μ (A) ≤ 1 for every A ∈ Σ of finite measure; (b) μ (A) ≥ 1 for every A ∈ Σ of positive measure, then there exist...
The converse problem for a generalized Dhombres functional equation
We consider the functional equation where is a given homeomorphism of an open interval and is an unknown continuous function. A characterization of the class of continuous solutions is given in a series of papers by Kahlig and Smítal 1998–2002, and in a recent paper by Reich et al. 2004, in the case when is increasing. In the present paper we solve the converse problem, for which continuous maps , where is an interval, there is an increasing homeomorphism of such that . We...