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Mediterranean Journal of Mathematics

, Volume 3, Issue 3–4, pp 363–382 | Cite as

On a Sequence of Positive Linear Operators Associated with a Continuous Selection of Borel Measures

  • Francesco AltomareEmail author
  • Vita Leonessa
Article

Abstract.

In this paper we introduce and study a new sequence of positive linear operators acting on the space of Lebesgue-integrable functions on the unit interval. These operators are defined by means of continuous selections of Borel measures and generalize the Kantorovich operators. We investigate their approximation properties by presenting several estimates of the rate of convergence by means of suitable moduli of smoothness. Some shape preserving properties are also shown.

Mathematics Subject Classification (2000).

41A10 41A25 41A36 

Keywords.

Borel measure positive approximation process Kantorovich operator Bernstein-Schnabl operator rate of convergence 

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Copyright information

© Birkhäuser Verlag, Basel/Switzerland 2006

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di BariBariItalia

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