Sahoo P. Mean Value Theorems and Functional Equations 1999

Textbook in PDF format

A comprehensive look at mean value theorems and their connection with functional equations. Besides the traditional Lagrange and Cauchy mean value theorems, it covers the Pompeiu and Flett mean value theorems, as well as extension to higher dimensions and the complex plane. Furthermore, the reader is introduced to the field of functional equations through equations that arise in connection with the many mean value theorems discussed.
Additive and Biadditive Functions
Lagrange's Mean Value Theorem and Related Functional Equations
Pompeiu's Mean Value Theorem and Associated Functional Equations
Two-Dimensional Mean Value Theorems and Functional Equations
Some Generalizations of Lagrange's Mean Value Theorem
Mean Value Theorems for Some Generalized Derivatives
Some Integral Mean Value Theorems and Related Topics