ON GENERALIZATIONS OF FLETT'S THEOREM.

In 1958 T. M. Flett proved a theorem which is a variant of the Lagrange mean value theorem; namely, let ƒ : [a, b] → R be a differentiable function in [a, b] and ƒ' (a) = ƒ' (b). Then there exists a number η ∈ (a, b) such that ƒ(η) - ƒ(a) = (η - a) - ƒ' (η). Manav Das, Thomas Riedel and Prasanna K. Sahoo have given generalizations of Flett's theorem for approximately differentiable functions. Here we provide generalizations of these theorems for some local S-systems. [ABSTRACT FROM AUTHOR]