A Characterization of Weighted Lp Approximations by the Gamma and the Post-Widder Operators

A characterization of weighted approximations by the Post-Widder and the Gamma operators

We present a characterization of the approximation errors of the PostWidder and the Gamma operators in Lp(0,∞), 1 ≤ p ≤ ∞, with a weight x for any real γ. Two types of characteristics are used – weighted Kfunctionals of the approximated function itself and the classical fixed step moduli of smoothness taken on a simple modification of it. AMS classification: 41A25, 41A27, 41A35, 41A36.

A characterization of weighted approximations by the Post-Widder and the Gamma operators, II

We present a characterization of the approximation errors of the PostWidder and the Gamma operators in Lp(0,∞), 1 ≤ p ≤ ∞, with a weight x0(1 + x)γ∞−γ0 with arbitrary real γ0, γ∞. Two types of characteristics are used – weighted K-functionals of the approximated function itself and the classical fixed step moduli of smoothness taken on simple modifications of it. 2000 Mathematics Subject Classi...

A Note on Weighted Composition Operators on L^p-Spaces

Hyers-Ulam Stability of Weighted Composition Operators on L^p-Spaces

Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm

Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...