Choquet Integral and Monotone Sublinear Operators
Springer International Publishing (Verlag)
978-3-031-71700-0 (ISBN)
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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.
Sorin G. Gal is Emeritus Professor at University of Oradea, Romania. His research focuses on real and complex analysis and approximation theory (in real, complex and quaternionic setting). He has published over 310 scientific articles in journals, ten books with prestigious international publishers and is associate managing editor of the journal Results in Mathematics.
Constantin P. Niculescu is Emeritus Professor at University of Craiova, Romania. His research focuses on real analysis, convexity, operator theory, ergodic theory and dynamical systems. He has published over 150 scientific articles , three books with prestigious international publishers and serves as associate editor of the journals Math. Inequalities and Appl., Annals of Functional Analysis and Proceedings of the Romanian Academy Series A: Mathematics, Physics, Technical Sciences, Information Science .
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.
| Erscheinungsdatum | 23.02.2025 |
|---|---|
| Reihe/Serie | Frontiers in Mathematics |
| Zusatzinfo | IX, 396 p. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 168 x 240 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Choquet Integrals • Functional analysis for monotone sublinear operators • Korovkin type theorems for monotone sublinear operators • Nonlinear Choquet type integral equations and operators • Quantitative approximations by Choquet integral operators |
| ISBN-10 | 3-031-71700-7 / 3031717007 |
| ISBN-13 | 978-3-031-71700-0 / 9783031717000 |
| Zustand | Neuware |
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