Estimate for the difference of operators having different basis functions

Abstract

Very recently Aral et al. (Anal Math Phys, 2018. https://doi.org/10.1007/s1332 ) established an estimate for the difference of two linear positive operators, but their result is valid for operators having same basis functions. In the present article, we study the approximation of difference of operators and establish a general estimate for the difference of those operators, which have different basis functions. In the end, we give examples of quantitative estimates for the difference between the Baskakov and Szasz–Mirakyan operators and between Szasz–Mirakyan and Baskakov–Kantorovich operators in terms of weighted modulus of continuity. Also, graphical representation is presented for such examples.