Choquet Integral and Monotone Sublinear Operators

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

Buch, Englisch, 343 Seiten, Format (B × H): 168 mm x 240 mm

Reihe: Frontiers in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Gal, Sorin G.

Niculescu, Constantin P.

Fachgebiete

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

Inhaltsverzeichnis

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.

Über Autor(innen)

Sorin G. Gal  was a Professor Emeritus at University of Oradea, Romania. His research focused 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 Professor Emeritus 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., Aequationes Mathematicae and Proceedings of the Romanian Academy Series A: Mathematics, Physics, Technical Sciences, Information Science.