均值定理及函数方程MEAN VALUE THEOREMS AND FUNCTIONAL EQUATIONS

Designed to introduce the simplicity & beauty of functional equations on one hand & the importance of the mean value theorem on the other.

Preface
Chapter I Additive and Biadditive Functions
　1.1 Continuous Additive Functions
　1.2 Discontinuous Additive Functions
　1.3 Other Criteria for Linearity
　1.4 Additive Functions on the Real and Complex Plane
　1.5 Biadditive Functions
　1.6 Some Open Problems
Chapter 2 Lagrange's Mean Value Theorem and Related Functional Equations
　2.1 Lagrange's Mean Value Theorem
　2.2 Applications of the MVT
　2.3 Associated Functional Equations
　2.4 The MVT for Divided Differences
　2.5 Limiting Behavior of Mean Values
　2.6 Cauchy's MVT and Functional Equations
　2.7 Some Open Problems
Chapter 3 Pompeiu's Mean Value Theorem and Associated Functional Equations
　3.1 Pompeiu's Mean Value Theorem
　3.2 Stamate Type Equations
　3.3 An Equation of Kuczma
　3.4 Equations Motivated by Simpson's Rule
　3.5 Some Generalizations
　3.6 Some Open Problems
Chapter 4 Two-dimensional Mean Value Theorems and Functional Equations
　4.1 MVTs for Functions in Two Variables
　4.2 Mean Value Type Functional Equations
　4.3 Generalized Mean Value Type Equations
　4.4 Cauchy's MVT for Functions in Two Variables
　4.5 Some Open Problems
Chapter 5 Some Generalizations of Lagrange's Mean Value Theorem
　5.1 MVTs for Real Functions
　5.2 MVTs for Real Valued Functions on the Plane
　5.3 MVTs for Vector Valued Functions on the Reals
　5.4 MVTs for Vector Valued Functions on the Plane
　5.5 MVTs for Functions on the Complex Plane
　5.6 A Conjecture of Furi and Martelli
Chapter 6 Mean Value Theorems for Some Generalized Derivatives
　6.1 Symmetric Differentiation of Real Functions
　6.2 A Quasi-Mean Value Theorem
　6.3 An Application
　6.4 Generalizations of MVTs
　6.5 Dini Derivatives of Real Functions
　6.6 MVTs for Nondifferentiable Functions
Chapter 7 Some Integral Mean Value Theorems and Related Topics
　7.1 The Integral MVT and Generalizations
　7.2 Integral Representation of Means
　7.3 Coincidence of Mean Values
　7.4 Some Open Problems
Bibliography
Index