Ordinary and fractional approximations by non-additive integrals, especially by integral approximators of Choquet, Silkret and Sugeno types, are a new trend in approximation theory. These integrals are only subadditive and only the first two are positive linear, and they produce very fast and flexible approximations based on limited data. The author presents both the univariate and multivariate cases. The involved set functions are much weaker forms of the Lebesgue measure and they were conceived to fulfill the needs of economic theory and other applied sciences. The approaches presented here are original, and all chapters are self-contained and can be read independently. Moreover, the book's findings are sure to find application in many areas of pure and applied mathematics, especially in approximation theory, numerical analysis and mathematical economics (both ordinary and fractional). Accordingly, it offers a unique resource for researchers, graduate students, and for coursework in the above-mentioned fields, and belongs in all science and engineering libraries.

Presents a range of original approaches to approximation All chapters are self-contained and can be read independently Provides a deeper formal analysis of several issues that are relevant to decision making, complex processes, systems modeling and control, and related areas Is suitable as a textbook for related graduate classes Obtains results that are sure to find application in many areas of pure and applied mathematics, especially in approximation theory, numerical analysis and mathematical economics (both ordinary and fractional)

Autorentext

George Anastassiou is Professor at the University of Memphis. Research interests include Computational analysis, approximation theory, probability, theory of moments. Professor Anastassiou has authored and edited several publications with Springer including "Fractional Differentiation Inequalities" (c) 2009, "Fuzzy Mathematics: Approximation Theory" (c) 2010, "Intelligent Systems: Approximation by Artificial Neural Networks" (c) 2014, "The History of Approximation Theory" (c) 2005, "Modern Differential Geometry in Gauge Theories" (c) 2006, and more. Razvan Alex Mezei received his PhD from the University of Memphis and currently holds an assistant professorship and Lenoir-Rhyne University, Hickory, North Carolina. He teaches mathematics as well as computer science/IT courses to undergraduates and is a computing sciences program coordinator. Mezei has extensive experience in computer programming and software development and has written several publications with George Anastassiou.

Inhalt

Approximation with rates by Kantorovich-Choquet quasi-interpolation neural network operators.- Approximation with rates by Perturbed Kantorovich-Choquet Neural Network Operators.- Approximation with rates by Shift Invariant Univariate Sublinear-Choquet Operators.- Approximation with rates by Shift Invariant Multivariate Sublinear-Choquet Operators.- Hardy type inequalities for Choquet integrals.- Quantitative Approximation by Choquet integrals.- Conformable Fractional Approximation by Choquet integrals.- Multivariate and Convex Quantitative Approximation by Choquet integrals.- Caputo and Canavati fractional Quantitative Approximation by Choquet integrals.- Mixed Conformable and Iterated fractional Quantitative Approximation by Choquet integrals.