Approximation by pseudo-linear operators
49
TL;DR: This paper proposes new, particular, pseudo-linear approximation operators, which are defined in some ordered semirings and obtains uniform approximation theorems of Weierstrass type, and Jackson-type error estimates in approximation by these operators.
read more
About: This article is published in Fuzzy Sets and Systems. The article was published on 01 Apr 2008. and is currently open access. The article focuses on the topics: Operator theory & Spectral theorem.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Approximation and Shape Preserving Properties of the Bernstein Operator of Max-Product Kind
TL;DR: For subclasses of functions 𝑓 including, for example, that of concave functions, the order of approximation 𝜔1(𝓓;1/𝑛), which for many functions � is essentially better than theOrder of approximation obtained by the linear Bernstein operators.
Approximation of fuzzy numbers by max-product Bernstein operators
TL;DR: This paper extends to an arbitrary compact interval the definition of the nonlinear Bernstein operators of max-product kind, by proving that their order of uniform approximation is the same as in the particular case of the unit interval, and proves that these operators preserve the quasi-concavity too.
33
Approximation and shape preserving properties of the nonlinear Favardsza-Szász-Mirakjan operator of max-product kind
TL;DR: In this paper, the Favard- Szasz-Mirakjan max-prod type operator is introduced and the question of the approximation order by this operator is raised.
Approximation and Shape Preserving Properties of the Nonlinear Meyer–König and Zeller Operator of Max-Product Kind
TL;DR: In this paper, the Meyer-Konig and Zeller max-product type operator is introduced and the question of the approximation order by this operator is raised and several shape preserving properties are obtained including the preservation of quasi-convexity.
25
Approximation by Shepard type pseudo-linear operators and applications to Image Processing
Barnabás Bede,Emil Daniel Schwab,Hajime Nobuhara,Imre J. Rudas +3 more
- 01 Jan 2009
TL;DR: Pseudo-linear approximation operators, including max-min, max-product Shepard type approximation operators together with Shepard operators based on pseudo-operations generated by an increasing continuous generator are investigated from the practical point of view in Image Processing.
15
References
A two-dimensional interpolation function for irregularly-spaced data
Donald S. Shepard
- 01 Jan 1968
TL;DR: In many fields using empirical areal data there arises a need for interpolating from irregularly-spaced data to produce a continuous surface as discussed by the authors, and it is assumed that a unique number (such as rainfall in meteorology, or altitude in geography) is associated with each data point.
5.1K
•Book
Lectures on Functional Equations and Their Applications
J. Aczel,Hansjorg Oser +1 more
- 01 Feb 2006
2.6K
On Grouping for Maximum Homogeneity
TL;DR: In this article, the authors present a practical procedure for grouping arbitrary numbers so that the variance within groups is minimized, including a description of an automatic computer program, given for problems up to the size where 200 numbers are to be placed in 10 groups.
860