Choquet Integral and Monotone Sublinear Operators
Series: Frontiers in Mathematics;
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Product details:
- Edition number 2024
- Publisher Springer Nature Switzerland
- Date of Publication 25 July 2026
- Number of Volumes 1 pieces, Book
- ISBN 9783031717000
- Binding Paperback
- No. of pages231 pages
- Size 240x168 mm
- Language English
- Illustrations XV, 231 p. 1 illus. Illustrations, black & white 700
Categories
Long description:
"
This book is primarily addressed to graduate students and researchers interested in exploring problems connected to mathematics, statistics, finance, insurance, climate change, and machine learning. The basic tools include the capacity theory and the Choquet integral, recognized for their usefulness in fields such as potential theory and decision making under risk and uncertainty. The book focuses on the authors' results on the relationship between the class of weakly nonlinear and monotone increasing operators and the class of Choquet-type integral operators. As an application, numerous new nonlinear extensions of the famous Korovkin theorem of approximation (as well as of Feller's scheme of approximation) are derived. The illustrations include the nonlinear operators of Bernstein-Kantorovich-Choquet, Szász-Mirakjan-Kantorovich-Choquet, Baskakov-Kantorovich-Choquet, and Picard-Choquet.
" MoreTable of Contents:
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Chapter 1: Preliminaries.- Chapter 2: The Choquet integral.- Chapter 3: The Lebesgue capacitary spaces,- Chapter 4: Weakly nonlinear operators acting on ordered Banach spaces.- Chapter 5: Korovkin’s theory in the framework of weakly nonlinear operators.
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