Article

ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 57, Issue 1, pp 39-66

First online:

On discrete q-beta operators

  • Vijay GuptaAffiliated withSchool of Applied Sciences, Netaji Subhash Institute of Technology Email author 
  • , P. N. AgrawalAffiliated withDepartment of Mathematics, Indian Institute of Technology Roorkee
  • , Durvesh Kumar VermaAffiliated withDepartment of Mathematics, Indian Institute of Technology Roorkee

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Abstract

The aim of the present paper is to introduce and study the q-analogue of discrete beta operators. First, we show some approximation properties of these operators. Then, we establish some global direct error estimates for the above operators using the second order Ditzian–Totik modulus of smoothness. Finally, we define and study the limit discrete q-beta operator.

Keywords

q-beta operators q-integer Ditzian–Totik modulus of smoothness

Mathematics Subject Classification (2000)

41A25 41A30