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Inequalities for Linear Positive Operators

Gancho Tachev


This survey paper grew out of a series of results, achieved at Duisburg in collaboration with mathematicians from Germany and Romania during my visits in the period of last seven years,1999-2005. Direct theorems for approximation of continuous real-valued functions by positive linear operators in terms of the second order modulus of smoothness are presented.Special emphasis is on the magnitude of the absolute constants appearing in the right-hand side of the inequalities. The degree of approximation for Bernstein operator, Schoenberg variation-diminishing spline operator and NURBS (non-uniform rational Bspline operator) is studied. Each of these three linear positive operators is a generalization of the preceding one and has an important applications in broad areas of mathematics such as real and functional analysis, approximation theory, numerical methods, computer-aided geometric design (CAGD), the theory of probabilities and mathematical statistics,geometry.


Linear Positive Operators,Degree of Approximation,Moduli of Smoothmess.

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