On a <Emphasis Type="Italic">q</Emphasis>-analogue of Stancu operators

This paper is concerned with a generalization in q-Calculus of Stancu operators. Involving modulus of continuity and Lipschitz type maximal function, we give estimates for the rate of convergence. A probabilistic approach is presented and approximation properties are established.     

On the variation detracting property of operators of Balázs and Szabados

In this note we spotlight the linear and positive operators of discrete type \({{{(R_n)}_{n\geqq1}}}\) known as Balázs–Szabados operators. We prove that this sequence enjoys the variation detracting property. The convergence in variation of \({{{(R_{n}f)}_{n\geqq1}}}\) to f is also proved. A generalization in Kantorovich sense is constructed and boundedness with respect to BV-norm is revealed.