On generalized Flett's mean value theorem

TL;DR

This paper offers a new proof of the generalized Flett's mean value theorem using only the original theorem, and establishes a Trahan-type condition for the general case.

Contribution

It provides a novel proof technique for the generalized Flett's mean value theorem and introduces a Trahan-type condition applicable in the general case.

Findings

New proof of generalized Flett's mean value theorem

Trahan-type condition established for the general case

Simplifies understanding of Flett's mean value theorem

Abstract

We present a new proof of generalized Flett's mean value theorem due to Pawlikowska (from Demonstratio Math. 1999) using only the original Flett's mean value theorem. Also, a Trahan-type condition is established in general case.