We estimate the degree of comonotone polynomial approximation of continuous functions f , on [−1,1], that change monotonicity s ≥ 1 times in the interval, when the degree of unconstrained polynomial… (More)

We survey developments, over the last thirty years, in the theory of Shape Preserving Approximation (SPA) by algebraic polynomials on a finite interval. In this article, “shape” refers to (finitely… (More)

We introduce new moduli of smoothness for functions f ∈ Lp[−1, 1]∩Cr−1(−1, 1), 1 ≤ p ≤ ∞, r ≥ 1, that have an (r − 1)st locally absolutely continuous derivative in (−1, 1), and such that φrf (r) is… (More)

When we approximate a continuous nondecreasing function f in ?1; 1], we wish sometimes that also the approximating polynomi-als be nondecreasing. However, this constraint restricts very much the… (More)

Estimating the degree of approximation in the uniform norm, of a convex function on a finite interval, by convex algebraic polynomials, has received wide attention over the last twenty years.… (More)

Let f be a continuous function on ?1; 1], which changes its monotonicity nitely many times in the interval, say s times. In the rst part of this paper we have discussed the validity of Jackson type… (More)

Our main interest in this paper is approximation of a continuous function, on a finite interval, which changes convexity finitely many times by algebraic polynomials which are coconvex with it. This… (More)

Let f 2 C ?1; 1] change its convexity nitely many times in the interval, say s times, at Y s : ?1 < y 1 < < y s < 1. We estimate the degree of approximation of f by polynomials of degree n, which… (More)

We discuss various properties of the new modulus of smoothness ω k,r (f, t)p := sup 0<h6t ‖W kh(·)∆khφ(·)(f , ·)‖Lp [−1,1], where φ(x) := √ 1− x2 and Wδ(x) = ( (1−x−δφ(x)/2)(1+x−δφ(x)/2) )1/2 .… (More)

2013 Federated Conference on Computer Science and…

2013

We consider the watermarking method based on a holographic transform domain image proposed by A. Bruckstein. Our testing showed that it is resistant not against all possible attacks declared by his… (More)