Volume 61, Issue 4

We introduce an extended cone algebra, which generalises a Bosbach’s cone algebra within the framework of extended BCK-algebras and show that every such an algebra is a direct product of an ℓ-group and a cone algebra of Bosbach.

Let F be a local complete field with discrete valuation, and let G be the group of F-points of a quasisplit group over F. Let ℬ be the Bruhat-Tits building of G and let A be an apartment of ℬ; we establish a link between bounded closed subsets of A and a special kind of functions on the relative root system Φ of G, which will be called strongly concave functions. This paper is devoted to the study of such functions.

A relation of weak majorization for n-dimensional real vectors is established, the result is then used to derive some inequalities involving the power mean, the arithmetic mean and the geometric mean in n variables.

In this paper we investigate some topological properties of solution sets of a differential equation of fractional order in Banach spaces. Our assumptions and proofs are expressed in terms of measures of noncompactness.

In this paper, we are concerned with oscillation of the third-order nonlinear neutral difference equation $\Delta (c_n [\Delta (d_n \Delta (x_n + p_n x_{n - \tau } ))]^\gamma ) + q_n f(x_{g(n)} ) = 0,n \geqslant n_0 ,$ where γ > 0 is the quotient of odd positive integers, c n, d n, p n and q n are positive sequences of real numbers, τ is a nonnegative integer, g(n) is a sequence of nonnegative integers and f ∈ C(ℝ,ℝ) such that uf(u) > 0 for u ≠ 0. Our results extend and improve some previously obtained ones. Some examples are considered to illustrate the main results.

We prove some direct and converse theorems of trigonometric approximation in weighted Orlicz spaces with weights satisfying so called Muckenhoupt’s A p condition.

In the present paper we propose a generalization of the Baskakov operators, based on q integers. We also estimate the rate of convergence in the weighted norm. In the last section, we study some shape preserving properties and the property of monotonicity of q-Baskakov operators.

A sharp estimate is given for the first order absolute moment of Meyer-König and Zeller operators M n. This estimate is then used to prove convergence of approximation of a class of absolutely continuous functions by the operators M n. The condition considered here is weaker than the condition considered in a previous paper and the rate of convergence we obtain is asymptotically the best possible.

We generalize the concept of Hecke pairs and study representations of the corresponding C*-algebra. We introduce the notions of covariant pairs and matrix unit pairs of representations in this general setting and show that covariant pairs are exactly faithful matrix unit pairs.

We show that the inverse limit and the orbit map commute for actions of compact groups on compact Hausdorff spaces.

In this paper, a size-biased Consul distribution (SBCOND) is defined. Recurrence relations for central moments and the moments about origin are obtained. Different estimation methods for the parameters of the model are discussed. A comparative analysis is done among the three different estimation methods and the proposed model is compared with the generalized logarithmic series distribution (GLSD) and simple Consul distribution.

The concept of the GAP-integral was introduced by the authors. In this paper some results on primitive for the GAP-integral are presented.