Volume 60, Issue 3

In this paper, properties of certain real-valued mappings Δ on binary systems X which satisfy versions of the triangle inequality are investigated. For example, via a quotient construction using Ker Δ = {x: Δ(x) = 0} it is shown that X/Ker Δ is a d-algebra if X is a d-algebra. In addition fuzzy versions of these triangular norms and their properties are considered as well. Finally boundedness conditions on Δ and a concept of magnitude are both introduced and some consequences are derived.

In two earlier papers [GAVRILUŢ, A.: A Gould type integral with respect to a multisubmeasure, Math. Slovaca 58 (2008), 1–20] and [Gavriluţ, A.: On some properties of the Gould type integral with respect to a multisubmeasure, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 52 (2006), 177–194], we defined and studied a Gould type integral for a real valued, bounded function with respect to a multisubmeasure having finite variation. In this paper, we introduce and study the properties of a Gould type integral in the general setting: the function may be unbounded and the variation of the multisubmeasure may be infinite.

In this paper we examine the regularity and pseudo-completeness of the sparse set topology introduced in [EAMES, W.: Local property of measurable sets, Canad. J. Math. 12 (1960), 632–640].

General conditions for the unique solvability of a non-linear nonlocal boundary-value problem for systems of non-linear functional differential equations are obtained.

In this paper the existence of a transition layer and unlayer solution for the stationary system ɛ 2Δu = f(u, υ), Δυ = g(u, υ) with x ∈ Ω ⊂ RN (N ≥ 2) is studied by using the degree-theoretical argument.

We prove an existence principle that would apply for elliptic problems with nonlinearity separating into a difference of derivatives of two convex functions in the case when the growth conditions are imposed only on the minuend term. We present abstract result and its application. We modify the so called dual variational method.

Sufficient conditions are obtained so that every solution of the neutral functional difference equation $$ \Delta ^m (y_n - p_n y_{\tau (n)} ) + q_n G(y_{\sigma (n)} ) - u_n H(y_{\alpha (n)} ) = f_n , $$ oscillates or tends to zero or ±∞ as n → ∞, where Δ is the forward difference operator given by Δx n = x n+1 − x n, p n, q n, u n, f n are infinite sequences of real numbers with q n > 0, u n ≥ 0, G,H ∈ C(ℝ,ℝ) and m ≥ 2 is any positive integer. Various ranges of {p n} are considered. The results hold for G(u) ≡ u, and f n ≡ 0. This paper corrects, improves and generalizes some recent results.

In this paper, we introduce the Euler sequence space e r(p) of nonabsolute type and prove that the spaces e r(p) and l(p) are linearly isomorphic. Besides this, we compute the α-, β- and γ-duals of the space e r(p). The results proved herein are analogous to those in [ALTAY, B.—BASŠAR, F.: On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math. 26 (2002), 701–715] for the Riesz sequence space r q(p). Finally, we define a modular on the Euler sequence space e r(p) and consider it equipped with the Luxemburg norm. We give some relationships between the modular and Luxemburg norm on this space and show that the space e r(p) has property (H) but it is not rotund (R).

Sufficient conditions for a random solution of random operator inclusions involving random multivalued operators satisfying a general contractive condition are obtained. A simultaneous random solution of the system of two random operator inclusions is also derived.

In the universal linear statistical model with the type II constraints, estimates of the unbiasedly estimable linear functions of the parameters of the mean value vector are given by special types of generalized matrix inverse. Since there exists many versions of such matrix inverse it is of some interest to check the unambiguity of obtained estimators. The aim of the paper is to find the best unbiased linear estimators of unbiasedly estimable functions and to show that they do not depend on the choice of the used generalized inverse of the matrices.