On the order of approximation of unbounded functions by the family of generalized linear positive operators

Abstract

In this study, a family of linear positive operators, which includes the sequence of linear positive operators built in a paper of A.D. Gadjiev and I.I. Ibragimov and later investigated by B. Wood and P. Radatz is defined and the order of convergence of these operators to continuous functions are studied. We give the estimate of difference |$L_{lambda $(f; x) - f(x)|, where $L_{lambda $ (f; x) is a family of linear positive operators, in terms of modulus of continuity of the mentioned function f.