Özarslan, Mehmet Ali; Duman, Oktay Smoothness properties of modified Bernstein-Kantorovich operators. (English) Zbl 1337.41012 Numer. Funct. Anal. Optim. 37, No. 1, 92-105 (2016). Summary: In this article, we consider modified Bernstein-Kantorovich operators and investigate their approximation properties. We show that the order of approximation to a function by these operators is at least as good as that of ones classically used. We obtain a simultaneous approximation result for our operators. Also, we prove two direct approximation results via the usual second-order modulus of smoothness and the second-order Ditzian-Totik modulus of smoothness, respectively. Finally, some graphical illustrations are provided. Cited in 2 ReviewsCited in 12 Documents MSC: 41A36 Approximation by positive operators 41A25 Rate of convergence, degree of approximation Keywords:Bernstein-Kantorovich operators; Ditzian-Totik modulus of smoothness; modulus of continuity; simultaneous approximation PDFBibTeX XMLCite \textit{M. A. Özarslan} and \textit{O. Duman}, Numer. Funct. Anal. Optim. 37, No. 1, 92--105 (2016; Zbl 1337.41012) Full Text: DOI References: [1] Agratini O., Rend. Circ. Mat. Palermo 68 (1) pp 229– (2002) [2] DOI: 10.4171/ZAA/1360 · Zbl 1140.41304 · doi:10.4171/ZAA/1360 [3] DOI: 10.1007/s00025-012-0236-z · Zbl 1272.41003 · doi:10.1007/s00025-012-0236-z [4] DOI: 10.1007/978-1-4612-1360-4 · doi:10.1007/978-1-4612-1360-4 [5] Bardaro C., Sampl. Theory Signal Image Process. 6 (1) pp 29– (2007) [6] Davis P. J., Interpolation and Approximation. (1975) · Zbl 0329.41010 [7] DOI: 10.1007/978-1-4612-4778-4 · doi:10.1007/978-1-4612-4778-4 [8] DOI: 10.1006/jath.1998.3212 · Zbl 0913.41008 · doi:10.1006/jath.1998.3212 [9] DOI: 10.1016/j.jmaa.2014.02.010 · Zbl 1312.41029 · doi:10.1016/j.jmaa.2014.02.010 [10] DOI: 10.2478/s11533-009-0061-0 · Zbl 1185.41021 · doi:10.2478/s11533-009-0061-0 [11] DOI: 10.1080/01630563.2011.580877 · Zbl 1236.41023 · doi:10.1080/01630563.2011.580877 [12] Guo S., Taiwanese J. Math. 11 (1) pp 161– (2007) [13] DOI: 10.5565/PUBLMAT_39295_04 · Zbl 0856.41015 · doi:10.5565/PUBLMAT_39295_04 [14] DOI: 10.1016/j.amc.2008.12.071 · Zbl 1183.41017 · doi:10.1016/j.amc.2008.12.071 [15] DOI: 10.1080/01630563.2014.951772 · Zbl 1315.41010 · doi:10.1080/01630563.2014.951772 [16] DOI: 10.1080/01630563.2013.806547 · Zbl 1286.41008 · doi:10.1080/01630563.2013.806547 [17] DOI: 10.1023/A:1024571126455 · Zbl 1027.41028 · doi:10.1023/A:1024571126455 [18] Mahmudov N. I., Studia Sci. Math. Hungar. 48 (2) pp 205– (2011) [19] DOI: 10.1080/01630563.2012.716806 · Zbl 1276.41015 · doi:10.1080/01630563.2012.716806 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.