Invariance of the Bajraktarević means with respect to the Beckenbach-Gini means

Assuming that the involved functions are three times differentiable, we determine all Bajraktarevi? means which are invariant respect to the mean-type mapping of the Beckenbach-Gini mean type. Some applications in iteration theory and functional equation are presented.     

On the Kluvánek construction of the Lebesgue integral with respect to a vector measure

The Kluvánek construction of the Lebesgue integral is extended in two directions. First, instead of a compact interval [a, b] in the real line an abstract non-empty set X is considered, instead of the ring generated by subintervals of [a, b] an arbitrary ring A of subsets of X. Secondly, instead of the length of intervals (λ([c, d]) = d?c) any vector measure λ: A→V is considered, where V is a Riesz space.     

On the convergence in L 1-norm of Cesàro means with respect to representative product systems

The aim of this paper is to prove that the Cesàro means of order α (0 < α < 1) of the Fourier series with respect to representative product systems converge to the function in L ¹-norm, only for certain values of α which depend on some parameter of the representative product system.     

Concavity of the complete elliptic integrals of the second kind with respect to Hölder means

In this paper, we establish a necessary and sufficient condition for the concavity of the complete elliptic integrals of the second kind with respect to Hölder means.     

Convexity of the complete elliptic integrals of the first kind with respect to Hölder means

In this paper, we establish a necessary and sufficient condition for the convexity of the complete elliptic integrals of the first kind with respect to Hölder means.     

On Cesáro summability of fourier series with respect to double complete orthonormal systems

Let {ϕn(x), n = 1, 2,...} be an arbitrary complete orthonormal system on the interval I:= [0, 1]which consists of a.e. bounded functions. Suppose that E ₀ ⊂ I ² is any Lebesgue measurable set such that μ₂ E ₀ > 0, and φ, φ(0) = 0, is an increasing continuous function on [0, ∞) with φ(u) = o(u ln u) as u → ∞. Then there exist a function f ∈ L¹(I ²) and a set E ₀ ^′ , ⊂ E ₀, μ₂ E ₀ ^′ > 0, such that

On the conditional expectation with respect to a sequence of independent σ-fields

Summary In the paper we characterize those sequences of random variables which are conditional expectations of a p-integrable random variable with respect to a given sequence of independent -fields.     

On the invariance equation for two-variable weighted nonsymmetric Bajraktarević means

Aequationes mathematicae - The purpose of this paper is to investigate the invariance of the arithmetic mean with respect to two weighted Bajraktarević means, i.e., to solve the functional...     

Inequalities for the generalized elliptic integrals with respect to Hölder means

In this paper, the authors prove some inequalities for the generalized elliptic integrals with respect to Hölder means.     

Halfconvex functions and equality of Daróczy–Páles conjugate means

Using some properties of halfconvex and halfconcave functions, we solve the equality problem for conjugate means introduced by Daróczy and Páles.     

On the (C, α)-means with respect to the Walsh system

In our main result we prove strong convergence theorems for Cesàro means (C, α) on the Hardy spaces H _1/(1+α), where 0 < α < 1.     

On the summability by Cesàro methods of double series with respect to block-orthonormal systems

The extension of the coefficient test of Menshov and Kaczmarz ensuring the almost everywhere (C, 1, 1)-((C, 1, 0) or (C, 0, 1)) summability of double series with respect to block-orthonormal systems is studied.     

On differentiability with respect to the initial data of the solution to an SDE with a Lévy noise and discontinuous coefficients

We construct a stochastic flow generated by an stochastic differential equation with its drift being a function of bounded variation and its noise being a stable process with exponent from (1,2). It is proved that the flow is non-coalescing and Sobolev differentiable with respect to the initial data. The representation for the derivative is given.     

On some properties of the ε-core of games with coalition structure

Chang [1991] stated some inclusion relation about kernel, reasonable set, and ε-core of games with coalition structure. We give counterexamples and modify erroneous results. Received: May 1997/Revised version: January 1999     

A characterization of tribes with respect to the Łukasiewicz t-norm

We give a complete characterization of tribes with respect to the ukasiewicz t-norm, i. e., of systems of fuzzy sets which are closed with respect to the complement of fuzzy sets and with respect to countably many applications of the ukasiewicz t-norm. We also characterize all operations with respect to which all such tribes are closed. This generalizes the characterizations obtained so far for other fundamental t-norms, e. g., for the product t-norm.     

On the Lovász theta function and some variants

The Lovász theta function of a graph is a well-known upper bound on the stability number. It can be computed efficiently by solving a semidefinite program (SDP). Actually, one can solve either of two SDPs, one due to Lovász and the other to Grötschel et al. The former SDP is often thought to be preferable computationally, since it has fewer variables and constraints. We derive some new results on these two equivalent SDPs. The surprising result is that, if we weaken the SDPs by aggregating constraints, or strengthen them by adding cutting planes, the equivalence breaks down. In particular, the Grötschel et al. scheme typically yields a stronger bound than the Lovász one.