Choquet Integral and Monotone Sublinear Operators / by Sorin G. Gal, Constantin P. Niculescu.

Format:

Book

Author/Creator:

Gal, Sorin G.

Series:

Frontiers in Mathematics, 1660-8054

Language:

English

Subjects (All):

Functional analysis.

Measure theory.

Approximation theory.

Functional Analysis.

Measure and Integration.

Approximations and Expansions.

Local Subjects:

Functional Analysis.

Measure and Integration.

Approximations and Expansions.

Physical Description:

1 online resource (394 pages)

Edition:

1st ed. 2026.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2026.

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.

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.

Notes:

Print version record.

ISBN:

9783031717017

OCLC:

1610749534