Mean Value Theorems and Functional Equations

This book takes 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 the 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. Ch. 1. Additive and biadditive functions -- ch. 2. Lagrange's mean value theorem and related functional equations -- ch. 3. Pompeiu's mean value theorem and associated functional equations -- ch. 4. Two-dimensional mean value theorems and functional equations -- ch. 5. Some generalizations of Lagrange's mean value theorem -- ch. 6. Mean value theorems for some generalized derivatives -- ch. 7. Some integral mean value theorems and related topics Designed to introduce the simplicity & beauty of functional equations on one hand & the importance of the mean value theorem on the other. The goal of this chapter is to present some results concerning additive and biadditive functions.