Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theor...

When an orthogonal array is projected on a small number of factors, as is done in screening experiments, the question of interest is the structure of the projected design, by which we mean its decomposition in terms of smaller arrays of the same strength. In this paper we investigate the decomposition of arrays of strength t having t + 1 factors. The decomposition problem is well-understood for...

We obtain the strong asymptotics of polynomials pn(λ), λ ∈ C, orthogonal with respect to measures in the complex plane of the form e 2s−tλs−tλs)dA(λ), where s is a positive integer, t is a complex parameter and dA stands for the area measure in the plane. Such problem has its origin from normal matrix models. We study the asymptotic behaviour of pn(λ) in the limit n,N → ∞ in such a way that n/N...

In this paper we consider random block matrices which generalize the classical Laguerre ensemble and the Jacobi ensemble. We show that the random eigenvalues of the matrices can be uniformly approximated by the roots of matrix orthogonal polynomials and obtain a rate for the maximum difference between the eigenvalues and the roots. This relation between the random block matrices and matrix orth...

Monotonicity of zeros of orthogonal Laurent polynomials associated with a strong distribution with respect to a parameter is discussed. A natural analog of a classical result of A. Markov is proved. Recent results of Ismail and Muldoon based on the Hellman-Feynman theorem are also extended to a monotonicity criterion for zeros of Laurent polynomials. Results concerning the behaviour of extreme ...