in this paper, a parameter uniform numerical method based on shishkin mesh is suggested to solve a system of second order singularly perturbed differential equations with a turning point exhibiting boundary layers. it is assumed that both equations have a turning point at the same point. an appropriate piecewise uniform mesh is considered and a classical finite difference scheme is applied on t...

We establish an integral formula for the duality between multilinear forms/homogeneous polynomials and tensor products for dual spaces with the approximation property and for which the injective tensor products of their preduals is separable and does not contain a copy of `1. We deduce some multilinear Bishop-Phelps-type results. Although spaces of multilinear forms and homogeneous polynomials ...

The aim of this note is to present an elementary proof of a variation of Harris’ ergodic theorem of Markov chains. This theorem, dating back to the fifties [Har56] essentially states that a Markov chain is uniquely ergodic if it admits a “small” set (in a technical sense to be made precise below) which is visited infinitely often. This gives an extension of the ideas of Doeblin to the unbounded...

In this paper, we obtain optimal perturbation bounds of the weighted Moore-Penrose inverse under the weighted unitary invariant norm, the weighted Q-norm and the weighted F -norm, and thereby extend some recent results.

In this paper, we obtain optimal perturbation bounds of the weighted Moore-Penrose inverse under the weighted unitary invariant norm, the weighted Q-norm and the weighted F -norm, and thereby extend some recent results.

Introduction In the rst part of the paper we study integral operators of the form (1) Kf(x) = v(x) x Z 0 k(x; y)u(y)f(y) dy; x > 0; where the real weight functions v(t) and u(t) are locally integrable and the kernel k(x; y) 0 satisses the following condition: there exists a constant D 1 such that Standard examples of a kernel k(x; y) 0 satisfying (2) are (i) k(x; y) = (x ? y) , 0 (ii) k(x; y) =...

We compute an asymptotic formula for the supremum of resolvent norm ||(ζ−T)−1|| over |ζ|≥1 and contractions T acting on n-dimensional Hilbert space, whose spectral radius does not exceed a given r∈(0,1). prove that this is achieved unit circle by analytic Toeplitz matrix.