Some inequalities for a Stancu type operator via (1,1) box convex functions

Authors

  • Ioan Gavrea Department of Mathematics, Technical University of Cluj Napoca, Romania
  • Daniel Ianoși Department of Mathematics, Technical University of Cluj Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat501-1242

Keywords:

Stancu operator, box convex functions
Abstract views: 164

Abstract

In this paper we introduce a Stancu type operator and we prove inequalities of Rașa's type.

Downloads

Download data is not yet available.

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

Downloads

Published

2021-11-19

How to Cite

Gavrea, I., & Ianoși, D. (2021). Some inequalities for a Stancu type operator via (1,1) box convex functions. J. Numer. Anal. Approx. Theory, 50(1), 52–59. https://doi.org/10.33993/jnaat501-1242

Issue

Section

Articles