Journal of East China Normal University(Natural Sc ›› 2018, Vol. 2018 ›› Issue (2): 31-40.doi: 10.3969/j.issn.1000-5641.2018.02.004

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Approximation properties of the left quasi-interpolants Gamma operators in Orlicz spaces

HAN Ling-xiong   

  1. College of Mathematics, Inner Mongolia University for the Nationalities, Tongliao Inner Mongolia 028043, China
  • Received:2017-03-22 Online:2018-03-25 Published:2018-03-22

Abstract: In order to reach better approximation degree, people start to study the quasiinterpolants of operators. In this paper, approximation properties of left quasi-interpolants Gamma operators are discussed by the tools of Ditizan-Totik modulus, K-functional, Hölder's inequality, Cauchy-Schwarz's inequality and Laguerre polynomials and so on. Then we obtain the direct, inverse and equivalence theorems which generalize the results of left quasi-interpolants Gamma operators in Lp space and improve the approximation properties of Gamma operators in Orlicz spaces.

Key words: left quasi-interpolants Gamma operator, K-functional, modulus of smoothness, equivalence theorem

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