Band 59, Heft 4

Ideals and atoms are studied by various authors from different point of views. In different algebras there are studied different ideals, but obtained results are similar. Below we present a new method of study of ideals in BZ-algebras. Using this method we describe the connection between ideals of various types.

Neutral elements and central elements are characterized in different classes of posets such as sectionally semi-complemented posets, atomistic posets etc.

We investigate a categorial duality between quasi MV-algebras (a variety of algebras arising from quantum computation and tightly connected with fuzzy logic) and a reflective subcategory of l-groups with strong units.

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form $$ (r(t)y')' + q(t)y' + p(t)f(y)g(y') = 0, t \geqslant t_0 , $$ where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.

This paper is concerned with a class of neutral difference equations of second order with positive and negative coefficients of the forms $$ \Delta ^2 (x_n \pm c_n x_{n - \tau } ) + p_n x_{n - \delta } - q_n x_{n - \sigma } = 0 $$ where τ, δ and σ are nonnegative integers and {p n}, {q n} and {c n} are nonnegative real sequences. Sufficient conditions for oscillation of the equations are obtained.

In this paper, sufficient conditions are obtained, so that the second order neutral delay differential equation $$ (r(t)(y(t) - p(t)y(t - \tau ))')' + q(t)G(y(h(t)) = f(t) $$ has a positive and bounded solution, where q, h, f ∈ C ([0, ∞), ℝ) such that q(t) ≥ 0, but ≢ 0, h(t) ≤ t, h(t) → ∞ as t → ∞, r ∈ C (1) ([0, ∞), (0, ∞)), p ∈ C (2) [0, ∞), ℝ), G ∈ C(ℝ, ℝ) and τ ∈ ℝ+. In our work r(t) ≡ 1 is admissible and neither we assume G is non-decreasing, xG(x) > 0 for x ≠ 0, nor we take G is Lipschitzian. Hence the results of this paper improve many recent results.

In this article we introduced the sequence spaces c I(p), c 0I(p), m I(p) and m 0I(p) for p = (p k), a sequence of positive real numbers. We study some algebraic and topological properties of these spaces. We prove the decomposition theorem and obtain some inclusion relations.

Using the principle of uniform boundedness in a strictly $$ \mathcal{N} $$-locally convex spaces, we establish a Banach-Steinhaus-type result for sequentially continuous linear operators.

We prove a fixed point theorem for contractive mappings of Boyd and Wong type in generalized metric spaces, a concept recently introduced in [BRANCIARI, A.: A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57 (2000), 31–37].

In this paper, the non-existence of limit cycles of a Liénard system ẋ = y−F(x), ẏ = −g(x) is discussed. By using the transformation y = z+ϕ(x) to the system, the new system has two special isoclines. We call the curves Vertical isocline or Horizontal isocline, respectively. It shall be shown that the existence of these isoclines play an important role in the non-existence of limit cycles of the system. The results are applied to many examples, and the known results are improved in certain cases.