Numer Algor https://doi.org/10.1007/s11075-018-0538-7 ORIGINAL PAPER Modified Kantorovich operators with better approximation properties Vijay Gupta 1 · Gancho Tachev 2 · Ana-Maria Acu 3 Received: 27 September 2017 / Accepted: 30 April 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In the present paper, we study a new kind of Bernstein-Kantorovich- type operators. Here, we discuss a uniform convergence estimate for this modified form. Also, some direct estimates, which involve the asymptotic-type results, are established. Some numerical examples which show the relevance of the results are considered. Keywords Approximation by polynomials · Kantorovich polynomials · Voronovskaja-type theorem Mathematics Subject Classification (2010) 41A25 · 41A36  Ana-Maria Acu acuana77@yahoo.com Vijay Gupta vijaygupta2001@hotmail.com Gancho Tachev gtt fte@uacg.bg 1 Department of Mathematics, Netaji Subhas Institute of Technology, Sector 3 Dwarka, New Delhi, 110078, India 2 Department of Mathematics, University of Architecture Civil Engineering and Geodesy, BG-1046, Sofia, Bulgaria 3 Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No.5-7, RO-550012 Sibiu, Romania