Choquet Integral and Monotone Sublinear Operators - Paperback

by Sorin G. Gal (Author), Constantin P. Niculescu (Author)

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.

Back Jacket

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, Sz?sz-Mirakjan-Kantorovich-Choquet, Baskakov-Kantorovich-Choquet, and Picard-Choquet.

Author Biography

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.