Mehmet Küçükaslan

Uniform Convergence of Some Extremal Polynomials in Domain with Corners on the Boundary

The aim of this paper is to investigate approximation properties of some extremal polynomials in , space. We are interested in finding approximation rate of extremal polynomials to Riemann function in and -norms on domains bounded by piecewise analytic curve.

Local one-sided porosity and pretangent spaces

Abstract For subsets of ℝ +

On the Asymptotic Behavior of p-Faber Polynomials for Domains with Piecewise Analytic Boundary

\mathbb{R}^{+}

METRIC SPACES WITH UNIQUE PRETANGENT SPACES. CONDITIONS OF THE UNIQUENESS

we consider the local right upper porosity and the local right lower porosity as elements of a cluster set of all porosity numbers. The use of a scaling function μ : ℕ → ℝ +

ON STATISTICAL CONVERGENCE AND STATISTICAL MONOTONICITY

{\mu:\mathbb{N}\to\mathbb{R}^{+}}

On the Statistical Convergence of Metric-Valued Sequences

provides an extension of the concept of porosity numbers on subsets of ℕ

On Statistical Boundedness of Metric Valued Sequences

{\mathbb{N}}

A generalization of deferred Cesáro means and some of their applications

. The main results describe interconnections between porosity numbers of a set, features of the scaling functions, and the geometry of so-called pretangent spaces to this set.

Uniform boundedness of pretangent spaces, local constancy of metric derivatives and strong right upper porosity at a point

Let 𝐺⊂ℂ be a domain bounded by a piecewise analytic Jordans curve L, and let 𝐹𝑛,𝑝 denote the p-Faber polynomials associated with G. We derive estimates of the form 𝐹𝑛,𝑝(𝑧)=𝑂(1/𝑛𝜂), (𝑛→∞) for 𝑧∈𝐺, where 𝜂 depends on geometric properties of L and the parameter p. Also, we show that O cannot be replaced by o in the relation given above.