Authors:
- First monograph in Statistical Approximation Theory and Fuzziness
- Self-contained book including a lot of applications within the framework of Statistical Approximation as well as a complete list of references
- Written by leading experts in the field
Part of the book series: Intelligent Systems Reference Library (ISRL, volume 14)
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Table of contents (18 chapters)
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Front Matter
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Back Matter
About this book
The main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been investigated in many fundamental areas of mathematics such as: measure theory, approximation theory, fuzzy logic theory, summability theory, and so on. In this monograph we consider this concept in approximating a function by linear operators, especially when the classical limit fails. The results of this book not only cover the classical and statistical approximation theory, but also are applied in the fuzzy logic via the fuzzy-valued operators. The authors in particular treat the important Korovkin approximation theory of positive linear operators in statistical and fuzzy sense. They also present various statistical approximation theorems for some specific real and complex-valued linear operators that are not positive. This is the first monograph in Statistical Approximation Theory and Fuzziness. The chapters are self-contained and several advanced courses can be taught.
The research findings will be useful in various applications including applied and computational mathematics, stochastics, engineering, artificial intelligence, vision and machine learning. This monograph is directed to graduate students, researchers, practitioners and professors of all disciplines.
Reviews
From the reviews:
“This is the first monograph in statistical approximation theory and fuzziness, which contains mostly the recent joint works of the authors … . The book consists of eighteen chapters which are self-contained and include many significant applications. … A complete list of references and a useful index are presented at the end of the book. This monograph is recommended to graduate students and researchers, in both pure and applied mathematics, specializing in summability and approximation theories.” (Cihan Orhan, Mathematical Reviews, Issue 2012 k)
Authors and Affiliations
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Department of Mathematical Sciences, The University of Memphis, Memphis, USA
George A. Anastassiou
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Department of Mathematics, TOBB Economics and Technology University, Sögütözü, Turkey
Oktay Duman
Bibliographic Information
Book Title: Towards Intelligent Modeling: Statistical Approximation Theory
Authors: George A. Anastassiou, Oktay Duman
Series Title: Intelligent Systems Reference Library
DOI: https://doi.org/10.1007/978-3-642-19826-7
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer Berlin Heidelberg 2011
Hardcover ISBN: 978-3-642-19825-0Published: 02 July 2011
Softcover ISBN: 978-3-642-26817-5Published: 15 July 2013
eBook ISBN: 978-3-642-19826-7Published: 06 April 2011
Series ISSN: 1868-4394
Series E-ISSN: 1868-4408
Edition Number: 1
Number of Pages: XVI, 236
Topics: Computational Intelligence, Artificial Intelligence, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences