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

If I ⊆ R is an interval, a ∈ I and f : I → R is n 1 times differentiable on I , then, in view of Taylor’s theorem, there exists a function c : I → I such that, for each x ∈ I, f (x) = n−1 ∑ k=0 f (k) (a) k! (x−a) + f (n) (c(x)) n! (x−a) . In this paper we study the behaviour of the derivatives c(p) and θ (p) of the functions c and θ , respectively, when x approaches a, where θ : I →]0,1[ is def...