We investigate weighted L p mean convergence of Grünwald interpolation operators based on the zeros of orthogonal polynomials with respect to a general weight and generalized Jacobi weights. We give necessary and sufficient conditions for such convergence for all continuous functions. 1. Introduction. In this paper, we study weighted L p (0 < p < ∞) mean con

‎Let $mathscr{L}$ be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space $mathbf{H}$ with ${rm dim}hspace{2pt}mathbf{H}geq 3$‎, ‎${rm Alg}mathscr{L}$‎ ‎the CSL algebra associated with $mathscr{L}$ and $mathscr{M}$ be an algebra containing ${rm Alg}mathscr{L}$‎. ‎This article is aimed at describing the form of‎ ‎additive mapppi...

The motive of this paper is to discuss the local convergence a two-step Newton-type method rate three for solving nonlinear equations in Banach spaces. It assumed that first order derivative operator satisfies generalized Lipschitz i.e., L-average condition. Also, some results on same spaces are established under assumption operators radius or center condition with weak particularly it L positi...

{ We consider the bilinear nite element method on a Shishkin mesh for the singularly perturbed elliptic boundary value problem ?" 2 (@ 2 u @x 2 + @ 2 u @y 2) + a(x; y)u = f(x; y) in two space dimensions. By using a very sophisticated asymptotic expansion of Han et al. 11] and the technique we used in 17], we prove that our method achieves almost second-order uniform convergence rate in L 2-norm...

In this paper we propose and analyze a new multiscale method for the wave equation. The proposed method does not require any assumptions on space regularity or scale-separation and it is formulated in the framework of the Localized Orthogonal Decomposition (LOD). We derive rigorous a priori error estimates for the L-approximation properties of the method, finding that convergence rates of up to...

This paper presents an information theory that is based on meanings and relationships of information. This paper first introduces the very basic concept in our approach, a binary relation contain between two pieces of information, which is based on inference between the two pieces of information. Then, based on the contain relation, this paper introduces two basic operations union and intersect...

Let X be an infinite-dimensional real reflexive Banach space with dual space X∗ and G⊂ X open and bounded. Assume that X and X∗ are locally uniformly convex. Let T : X ⊃ D(T) → 2X be maximal monotone and C : X ⊃ D(C) → X∗ quasibounded and of type (S̃+). Assume that L ⊂ D(C), where L is a dense subspace of X , and 0 ∈ T(0). A new topological degree theory is introduced for the sum T +C. Browder’s...

in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.

in this paper the author considers a general method, based on time domain samples for spectral manipulation of time limited signals. first, the original signal is divided into some frames in the time domain. then, by presenting a suitable theoretical and computational algorithm, and using a method for improving the speed of convergence, we find the local bandwidth of each frame; thereby, each f...