Abstract

In this paper, we study the approximation on differences of two different positive linear operators (generalized P\v{a}lt\v{a}nea type operators and M. Heilmann type operators) with same basis functions. We estimates a quantitative difference of these operators in terms of modulus of continuity and Peetre's $K$-functional. We represent the rate of convergence, using modulus of continuity and Peetre's $K$-functional. Also, we represent Heilmann-type operators in terms of hypergeometric series.

Keywords: Difference operators; generalized P\v{a}lt\v{a}nea type operators; Heilmann type operators; modulus of continuity, rate of convergence.

MSC: 41A25, 26A15,41A30

Pages:  101$-$109     

Volume  74 ,  Issue  2 ,  2022