Description 
xiv, 237 pages : illustrations ; 24 cm 
Contents 
Machine derived contents note: 1. Introduction 1  1.1 Historical notes 1  1.2 Preliminaries 6  1.3 tnorms and snorms 9  1.4 Copulas 17  2. Representation theorems for associative functions 23  2.1 Continuous, Archimedean tnorms 23  2.2 Additive and multiplicative generators 38  2.3 Extension to arbitrary closed intervals 51  2.4 Continuous, nonArchimedean tnorms 57  2.5 Noncontinuous tnorms 64  2.6 Families of tnorms 70  2.7 Other representation theorems 81  2.8 Related functional equations. 93  3. Functional equations involving tnorms 99  3.1 Simultaneous associativity 99  3.2 nduality 110  3.3 Simple characterizations of Min 127  3.4 Homogeneity 129  3.5 Distributivity 134  3.6 Conical tnorms 137  3.7 Rational Archimedean tnorms 143  3.8 Extension and sets of uniqueness 151  4. Inequalities involving tnorms 173  4.1 Notions of concavity and convexity 173  4.2 The dominance relation 182  4.3 Uniformly close associative functions 189  4.4 Serial iterates and ncopulas 194  4.5 Positivity 203 
Summary 
"This book presents the foundations of the subject of associative functions on real intervals. It brings together results that have been widely scattered in the literature and adds much new material. In the process, virtually all the standard techniques for solving functional equations in one and several variables come into play. Thus, the book can serve as an advanced undergraduate or graduate text on functional equations."BOOK JACKET 
Bibliography 
Includes bibliographical references (pages 223234) and index 
Subject 
Associative law (Mathematics)


Associative law (Mathematics)  Study and teaching  Textbooks.


Functional equations  Study and teaching  Textbooks.


Functional equations.


Mathematical analysis  Study and teaching  Textbooks.


Mathematical analysis.

Genre/Form 
Textbooks.

Author 
Frank, Maurice J.


Schweizer, B. (Berthold)

LC no. 
2006284938 
ISBN 
9812566716 
