Variation diminishing-type properties for multivariate sampling Kantorovich operators

被引:12
作者
Angeloni, Laura [1 ]
Costarelli, Danilo [1 ]
Seracini, Marco [1 ]
Vinti, Gianluca [1 ]
Zampogni, Luca [1 ]
机构
[1] Univ Perugia, Dept Math & Comp Sci, Via Vanvitelli 1, I-06123 Perugia, Italy
来源
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA | 2020年 / 13卷 / 04期
关键词
Multivariate generalized sampling Kantorovich series; Variation-diminishing type property; Averaged type kernel; Smoothing in digital image processing; Product kernel; INTEGRAL-OPERATORS; CONVERGENCE; APPROXIMATION; GAUGE;
D O I
10.1007/s40574-020-00256-3
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we establish a variation-diminishing type estimate for the multivariate Kantorovich sampling operators with respect to the concept of multidimensional variation introduced by Tonelli. A sharper estimate can be achieved when step functions with compact support (digital images) are considered. Several examples of kernels have been presented.
引用
收藏
页码:595 / 605
页数:11
相关论文
共 50 条
[41]   Kantorovich Variant of the Blending Type Bernstein Operators [J].
Baytunc, Erdem ;
Gezer, Halil ;
Aktuglu, Huseyin .
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2024, 50 (06)
[42]   On the convergence properties of sampling Durrmeyer-type operators in Orlicz spaces [J].
Costarelli, Danilo ;
Piconi, Michele ;
Vinti, Gianluca .
MATHEMATISCHE NACHRICHTEN, 2023, 296 (02) :588-609
[43]   Quantitative estimates for perturbed sampling Kantorovich operators in Orlicz spaces [J].
Costarelli, Danilo ;
De Angelis, Eleonora ;
Vinti, Gianluca .
DEMONSTRATIO MATHEMATICA, 2024, 57 (01)
[44]   CONVERGENCE THEOREMS IN ORLICZ AND BOGEL CONTINUOUS FUNCTIONS SPACES BY MEANS OF KANTOROVICH DISCRETE TYPE SAMPLING OPERATORS [J].
Ayan, Serkan ;
Ispir, Nurhayat .
MATHEMATICAL FOUNDATIONS OF COMPUTING, 2023, 6 (03) :354-368
[45]   Some density results by deep Kantorovich type neural network operators [J].
Sharma, Manju ;
Singh, Uaday .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 533 (02)
[46]   New Kantorovich-type Szász-Mirakjan Operators [J].
Mahmudov, Nazim I. ;
Kara, Mustafa .
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2024, 50 (05)
[47]   Asymptotic properties of Urysohn type generalized sampling operators [J].
Karsli, H. .
CARPATHIAN MATHEMATICAL PUBLICATIONS, 2021, 13 (03) :631-641
[48]   Convergence properties of Durrmeyer-type sampling operators [J].
Sharma, Vaibhav ;
Gupta, Vijay .
COMPUTATIONAL & APPLIED MATHEMATICS, 2024, 43 (07)
[49]   Bivariate α,q-Bernstein-Kantorovich Operators and GBS Operators of Bivariate α,q-Bernstein-Kantorovich Type [J].
Cai, Qing-Bo ;
Cheng, Wen-Tao ;
Cekim, Bayram .
MATHEMATICS, 2019, 7 (12)
[50]   Estimations for the convex modular of the aliasing error of nonlinear sampling Kantorovich operators [J].
Costarelli, Danilo ;
Natale, Mariarosaria ;
Vinti, Gianluca .
NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2025, 30 (02) :270-290