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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.
List of contents
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.
About the author
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.
Summary
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.
