Some inequalities for a Stancu type operator via (1,1) box convex functions
DOI:
https://doi.org/10.33993/jnaat501-1242Keywords:
Stancu operator, box convex functionsAbstract
In this paper we introduce a Stancu type operator and we prove inequalities of Rașa's type.Downloads
References
U. Abel,An inequality involving Bernstein polynomials, J. Approx. Theory, 222 (2017), pp. 1–7, https://doi.org/10.1016/j.jat.2017.05.006
U. Abel, D. Leviatan, An extension of Rasa’s conjecture to q-monotone functions, Results Math., 75(4) (2020), pp. 181–193, https://doi.org/10.1007/s00025-020-01308-y
S. Gal, Shape-Preserving Approximation by Real and Complex Polynomials, Birkhauser, Boston, 2008, https://doi.org/10.1007/978-0-8176-4703-2
S. Gal, P. Niculescu, A new look at Popoviciu’s concept for functions of two variables, J. Math. Anal. Appl., 479(2019), pp. 903–925, https://doi.org/10.1016/j.jmaa.2019.06.057
B. Gavrea, On a convexity problem in connection with some linear operators, J. Math. Anal. Appl., 461 (2018), pp. 319–332, https://doi.org/10.1016/j.jmaa.2018.01.010
B. Gavrea, On a convexity problem with applications to Mastroianni type operators, Math. Inequal. Appl., 23 (2020), pp. 765–773, https://doi.org/10.7153/mia-2020-23-64
B. Gavrea, I. Gavrea, An inequality involving Bernstein polynomials and box-convex functions, submitted.
J. Mrowiec, T. Rajba, S. Wasowicz, A solution to the problem of Rasa connected with Bernstein polynomials, J. Math. Anal. Appl., 446 (2017), pp. 864–878, https://doi.org/10.1016/j.jmaa.2016.09.009
T. Popoviciu, Sur quelques proprietes des fonctions d’une ou de deux variables reelles, Theses de l’entre-deux-guerres, Faculte des Sciences de Paris, (1933).
I. Rasa, Problem 2, pp. 164. In: Report of meeting in: Conference on Ulam’s Type Stability, Rytro, Poland, June 2–6, 2014, Ann. Paedagog. Croc. Stud. Math., 13 (2014), pp. 139-169, https://doi.org/10.2478/aupcsm-2014-0011
D.D. Stancu, On a generalization of the Bernstein polynomials, Studia Univ. Babes-Bolyai Math (Cluj), 14 (1969), pp. 31–45.
D.D. Stancu, Approximation of functions by means of a new generalized Bernstein operator, Calcolo, 20 (1983), pp. 211–229, https://doi.org/10.1007/BF02575593
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