The goal of the paper is to present some results concerning the approximation of convex functions by linear positive operators. First, one recalls some results concerning the univariate real valued convex functions. Next, one presents the notion of higher order convexity introduced by Popoviciu [Popoviciu, T., Sur quelques propriétées des fonctions d’une ou deux variable réelles, PhD Thesis, La Faculte des Sciences de Paris, 1933 (June)]. The Popoviciu’s famous theorem for the representation of linear functionals associated to convex functions of th order (with the proof of author) is also presented. Finally, applications of the convexity to study the monotonicity of sequences of some linear positive operators and also mean value theorems for the remainder term of some approximation formulas based on linear positive operators are presented.
On the approximation of convex functions using linear positive operators
Bărbosu, Dan
Full PDF
creative_2017_26_2_137_143Search…
Magazine Issues
- Vol 33/2024 no. 2 (14)
- Vol 33/2024 no. 1 (11)
- Vol 32/2023 no. 2 (12)
- Vol 32/2023 no. 1 (12)
- Vol 31/2022 no. 2 (12)
- Vol 31/2022 no. 1 (13)
- Vol 29/2020 no. 2 (16)
- Vol 30/2021 no. 1 (14)
- Vol 30/2021 no. 2 (12)
- Vol 29/2020 no. 1 (13)
- Vol 28/2019 no. 2 (14)
- Vol 28/2019 no. 1 (13)
- Vol 27/2018 no. 2 (14)
- Vol 27/2018 no. 1 (13)
- Vol 26/2017 no. 3 (13)
- Vol 26/2017 no. 2 (13)
- Vol 26/2017 no. 1 (14)
- Vol 25/2016 no. 2 (15)
- Vol 25/2016 no. 1 (15)
- Vol 24/2015 no. 2 (17)
- Vol 24/2015 no. 1 (13)
- Vol 23/2014 no. 2 (17)
- Vol 23/2014 no. 1 (15)
- Vol 22/2013 no. 2 (14)
- Vol 22/2013 no. 1 (16)
- Vol 21/2012 no. 2 (15)
- Vol 21/2012 no. 1 (14)
- Vol 20/2011 no. 2 (14)
- Vol 20/2011 no. 1 (15)
- Vol 19/2010 no. 2 (18)
- Vol 19/2010 no. 1 (13)
- Vol 18/2009 no. 2 (17)
- Vol 18/2009 no. 1 (14)
- Vol 17/2008 no. 3 (41)
- Vol 17/2008 no. 2 (17)
- Vol 17/2008 no. 1 (23)
- Vol 16/2007 (22)
- Vol 15/2006 (21)
- Vol 14/2005 (20)
- Vol 13/2004 (20)
- Vol 12/2003 (19)
- Vol 11/2002 (22)
- Vol 10/2001 (25)
- Vol 09/2000 (23)
- Vol 08/1999 (19)
- Vol 07/1998 (17)
- Vol 06/1997 (12)
- Vol 05/1996 (22)
- Vol 04/1995 (20)
- Vol 03/1994 (14)
- Vol 02/1993 (18)
- Vol 01/1992 (12)
- Uncategorized (0)
Recently posted
- Power Domination in Generalized Mycielskian of Cycles
- Fixed point theorem for composition of multivalued and single-valued mappings in Banach spaces
- Initial Value Problem for Hybrid Improved Conformable Fractional Differential Equations with Retardation and Anticipation
- On a Subclass of Meromorphic Functions Defined by a Differential Operator on Hilbert Space
- Countably Many Positive Symmetric Solutions For Sturm Liouville Type Boundary Conditions Of Second Order Iterative System
- On the derived numbers of a real function
- Some considerations about l'Hôpital-type rules for the monotonicity
- On Minimum Second neighborhood Degree Energy of Graphs
- Preserver Problems on Infinite Divisibility and Separability
- A Note on Moritoh Transforms