A Study on Flett’s Mean Value Theorem

Abstract

The aim of this study is to evaluate the parallels between the results of Flett's Mean Value Theorem, Lagrange's Mean Value Theorem, and Rolle's Theorem, as well as their geometrical significance. It also covers Thomas M. Flett's 1958 Mean Value Theorem of Differential and Integral Calculus and its various extensions. We intend to present a thorough analysis of various (existing as well as new) adequate conditions for this theorem's validity because it is a topic of interest in many areas of mathematics, including functional equations.