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Mediterranean Journal of Mathematics

, Volume 12, Issue 1, pp 21–35 | Cite as

Summability Process by Mastroianni Operators and Their Generalizations

  • Oktay Duman
Article
  • 158 Downloads

Abstract

In this paper, we prove a general Korovkin-type approximation theorem for the Mastroianni operators using a regular summability process with non-negative entries. We also obtain some useful estimates via the modulus of continuity and the second modulus of smoothness. Furthermore, we construct a sequence of Szász–Mirakjan type operators satisfying a Voronovskaja-type property such that it is possible to approximate a function by these operators in the sense of summation process, although their classical approximation fails.

Mathematics Subject Classification (2010)

40C05 40D05 40G05 41A36 

Keywords

Summability process Cesàro summability Almost convergence Mastroianni operators Korovkin-type theorems Voronovskaja-type theorem 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsTOBB Economics and Technology UniversitySöğütözüTurkey

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