Anal.Math.Phys. https://doi.org/10.1007/s13324-018-0227-7 On differences of linear positive operators Ali Aral 1 · Daniela Inoan 2 · Ioan Ra¸ sa 2 Received: 30 September 2017 / Revised: 22 February 2018 / Accepted: 7 April 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract In this paper we consider two different general linear positive operators defined on unbounded interval and obtain estimates for the differences of these oper- ators in quantitative form. Our estimates involve an appropriate K -functional and a weighted modulus of smoothness. Similar estimates are obtained for Chebyshev func- tional of these operators as well. All considerations are based on rearrangement of the remainder in Taylor’s formula. The obtained results are applied for some well known linear positive operators. Keywords K -functionals · Weighted moduli of smoothness · Chebyshev functional Mathematics Subject Classification Primary 41A36; Secondary 41A25 1 Introduction In the present paper we deal with Lupa¸ s’ problem from a more general point of view and give answers to this problem with some applications using well known operators. The question introduced by him is related to an estimate of the difference B Ali Aral aliaral73@yahoo.com Daniela Inoan daniela.inoan@math.utcluj.ro Ioan Ra¸ sa ioan.rasa@math.utcluj.ro 1 Department of Mathematics, Kırıkkale University, 71450 Yah¸ sihan, Kırıkkale, Turkey 2 Department of Mathematics, Technical University of Cluj-Napoca, Cluj, Romania