Choquet Integrals and Monotone Sublinear Operators

2025
ISBN: 978-3-031-71700-0
Verlag: Birkhäuser

Buch, Englisch, 396 Seiten, Format (B × H): 168 mm x 240 mm

Reihe: Frontiers in Mathematics

Mainly addressed to researchers in the fields of generalized measure theory, nonlinear integrals, nonlinear functional analysis, and nonlinear approximation theory, this book is based mainly on the authors’ results. While the Choquet integral has proven to be powerful and useful in cooperative games, decision theory, finance, economics, insurance, pattern recognition, artificial intelligence, and automated reasoning, these applications are not the focus in this monograph. Instead, the special properties of Choquet’s integral, inspired the study of various aspects for the class of monotone sublinear operators (more general than the positive linear operators) on Banach ordered spaces, as for example Korovkin-type results. The main ideas in this book also include the replacement in various known mathematical concepts, of the classical linear Lebesgue integral by the nonlinear (sublinear and monotone)  Choquet integral and to study the new obtained concepts.

Zielgruppe

Research

Autoren/Hrsg.

Gal, Sorin G.

Niculescu, Constantin P.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

Choquet Integral.- Choquet-Bochner Integral.- Choquet Integral in Capacity.- Choquet-Stieltjes Integrals on Intervals.- Other Generalizations.- Choquet Type Integral Equations and Operators.- Constructive Approximation Involving Choquet Integrals.- Korovkin-Type Theorems for Monotone Sublinear Operators.- A Few Elements of Functional Analysis for Sublinear and Monotone Operators.

Über Autor(innen)

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 .