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Shape-preserving properties of a new family of generalized Bernstein operators.
- Source :
-
Journal of Inequalities & Applications . 9/14/2018, Vol. 2018 Issue 1, p1-1. 1p. - Publication Year :
- 2018
-
Abstract
- In this paper, we introduce a new family of generalized Bernstein operators based on q integers, called (α,q)<inline-graphic></inline-graphic>-Bernstein operators, denoted by Tn,q,α(f)<inline-graphic></inline-graphic>. We investigate a Kovovkin-type approximation theorem, and obtain the rate of convergence of Tn,q,α(f)<inline-graphic></inline-graphic> to any continuous functions f. The main results are the identification of several shape-preserving properties of these operators, including their monotonicity- and convexity-preserving properties with respect to f(x)<inline-graphic></inline-graphic>. We also obtain the monotonicity with n and q of Tn,q,α(f)<inline-graphic></inline-graphic>. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10255834
- Volume :
- 2018
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Inequalities & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 131779725
- Full Text :
- https://doi.org/10.1186/s13660-018-1821-9