Max-product shepard approximation operators

Barnabás Bede; Hajime Nobuhara; János Fodor; Kaoru Hirota

Max-product shepard approximation operators

Barnabás Bede, Hajime Nobuhara, János Fodor, Kaoru Hirota

Research output: Contribution to conference › Paper › peer-review

Abstract

In crisp approximation theory the operations that are used are only the usual sum and product of reals. We propose the following problem: are sum and product the only operations that can be used in approximation theory? As an answer to this problem we propose max-product Shepard Approximation operators and we prove that these operators have very similar properties to those provided by the crisp approximation theory. In this sense we obtain uniform approximation theorem of Weierstrass type, and Jackson-type error estimate in approximation by these operators.

Original language	English
Publication status	Published - 2005
Externally published	Yes
Event	3rd Serbian-Hungarian Joint Symposium on Intelligent Systems, SISY 2005 - Subotica, Serbia Duration: 31 Aug 2005 → 1 Sept 2005

Conference

Conference	3rd Serbian-Hungarian Joint Symposium on Intelligent Systems, SISY 2005
Country/Territory	Serbia
City	Subotica
Period	31/08/05 → 1/09/05

Cite this

@conference{fda7ecf61c0447dc9e9d3b2f2b28808a,

title = "Max-product shepard approximation operators",

abstract = "In crisp approximation theory the operations that are used are only the usual sum and product of reals. We propose the following problem: are sum and product the only operations that can be used in approximation theory? As an answer to this problem we propose max-product Shepard Approximation operators and we prove that these operators have very similar properties to those provided by the crisp approximation theory. In this sense we obtain uniform approximation theorem of Weierstrass type, and Jackson-type error estimate in approximation by these operators.",

author = "Barnab{\'a}s Bede and Hajime Nobuhara and J{\'a}nos Fodor and Kaoru Hirota",

year = "2005",

language = "English",

note = "3rd Serbian-Hungarian Joint Symposium on Intelligent Systems, SISY 2005 ; Conference date: 31-08-2005 Through 01-09-2005",

}

TY - CONF

T1 - Max-product shepard approximation operators

AU - Bede, Barnabás

AU - Nobuhara, Hajime

AU - Fodor, János

AU - Hirota, Kaoru

PY - 2005

Y1 - 2005

N2 - In crisp approximation theory the operations that are used are only the usual sum and product of reals. We propose the following problem: are sum and product the only operations that can be used in approximation theory? As an answer to this problem we propose max-product Shepard Approximation operators and we prove that these operators have very similar properties to those provided by the crisp approximation theory. In this sense we obtain uniform approximation theorem of Weierstrass type, and Jackson-type error estimate in approximation by these operators.

AB - In crisp approximation theory the operations that are used are only the usual sum and product of reals. We propose the following problem: are sum and product the only operations that can be used in approximation theory? As an answer to this problem we propose max-product Shepard Approximation operators and we prove that these operators have very similar properties to those provided by the crisp approximation theory. In this sense we obtain uniform approximation theorem of Weierstrass type, and Jackson-type error estimate in approximation by these operators.

UR - http://www.scopus.com/inward/record.url?scp=84943371552&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:84943371552

T2 - 3rd Serbian-Hungarian Joint Symposium on Intelligent Systems, SISY 2005

Y2 - 31 August 2005 through 1 September 2005

ER -

Max-product shepard approximation operators

Abstract

Conference

Other files and links

Fingerprint

Cite this