Approximation properties of a family of integral type operators

Abstract

In this paper we consider a general class of linear positive processes of integral type. These operators act on functions defined on unbounded interval. Among the particular cases included are Durrmeyer–Jain operators, Păltănea–Szász–Mirakjan operators and operators using Baskakov–Szász type bases. We focus on highlighting some approximation targeting different classes of functions. The main working tools are Bohman–Korovkin theorem, weighted K-functionals and moduli of smoothness.

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Correspondence to Octavian Agratini.

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Agratini, O. Approximation properties of a family of integral type operators. Positivity 25, 97–108 (2021). https://doi.org/10.1007/s11117-020-00752-y

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Keywords

  • Positive linear operator
  • Weighted K-functional
  • Modulus of smoothness
  • Durrmeyer–Jain operator

Mathematics Subject Classification

  • 41A36
  • 41A25