A Unified Approach for Nonlinear Kantorovich-Type Operators

Flavia Ventriglia; Gianluca Vinti

Bollettino dell'Unione Matematica Italiana (2013)

  • Volume: 6, Issue: 3, page 715-724
  • ISSN: 0392-4041

Abstract

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In this paper we introduce some important results on the approximation by series and their generalizations for integral operators. In particular, we show some new results for nonlinear Kantorovich-type operators, contained in a recent publication, and several graphical examples.

How to cite

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Ventriglia, Flavia, and Vinti, Gianluca. "A Unified Approach for Nonlinear Kantorovich-Type Operators." Bollettino dell'Unione Matematica Italiana 6.3 (2013): 715-724. <http://eudml.org/doc/294048>.

@article{Ventriglia2013,
abstract = {In this paper we introduce some important results on the approximation by series and their generalizations for integral operators. In particular, we show some new results for nonlinear Kantorovich-type operators, contained in a recent publication, and several graphical examples.},
author = {Ventriglia, Flavia, Vinti, Gianluca},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {715-724},
publisher = {Unione Matematica Italiana},
title = {A Unified Approach for Nonlinear Kantorovich-Type Operators},
url = {http://eudml.org/doc/294048},
volume = {6},
year = {2013},
}

TY - JOUR
AU - Ventriglia, Flavia
AU - Vinti, Gianluca
TI - A Unified Approach for Nonlinear Kantorovich-Type Operators
JO - Bollettino dell'Unione Matematica Italiana
DA - 2013/10//
PB - Unione Matematica Italiana
VL - 6
IS - 3
SP - 715
EP - 724
AB - In this paper we introduce some important results on the approximation by series and their generalizations for integral operators. In particular, we show some new results for nonlinear Kantorovich-type operators, contained in a recent publication, and several graphical examples.
LA - eng
UR - http://eudml.org/doc/294048
ER -

References

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  1. HIGGINS, J.R., Five short stories about the cardinal series, Bull. Amer. Math. Soc., 12 (1) (1985), 45-89. Zbl0562.42002MR766960DOI10.1090/S0273-0979-1985-15293-0
  2. BUTZER, P.L., A survey of the Whittaker-Shannon sampling theorem and some of its extentions, J. Math. Res. Exposition, 3 (1983), 185-212. Zbl0523.94003MR724869
  3. BARDARO, C. - MUSIELAK, J., VINTI, G., Nonlinear integral operators and applications, de Gruyter Series in Nonlinear Analysis and Applications, vol. 9, Walter de Gruyter and Co., Berlin, 2003. Zbl1030.47003MR1994699DOI10.1515/9783110199277
  4. BARDARO, C. - BUTZER, P.L. - STENS, R.L. - VINTI, G., Kantorovich-type generalized sampling series in the setting of Orlicz spaces, Sampling Theory in Signal and Image Processing, 6 (1) (2007), 29-52. Zbl1156.41307MR2296881
  5. VENTRIGLIA, F. - VINTI, G., A unified approach for the convergence on nonlinear Kantorovich-Type operators, to appear. Zbl1300.41017MR3235270
  6. VINTI, G., ZAMPOGNI, L., Approximation by means of nonlinear Kantorovich sampling type operators in Orlicz spaces, J. of Approximation Theory, 161 (2009), 511-528. Zbl1183.41016MR2563068DOI10.1016/j.jat.2008.11.011

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