Extended Generalized Mean Value Theorem for Functions of One Variable

Abstract

In this manuscript, we state and prove a theorem of a similar flavour to the Generalized Mean Value Theorem for functions of one variable. For lack of a better term, we call the theorem ``Extended Generalized Mean Value Theorem'' and we abbreviate it EGMVT.In addition, we apply Rolle's Theorem to prove the theorem. Also, we deduce some corollaries for Mean Value Theorems. In addition, the EGMVT is verified by use of an example.

Extended Generalized Flett's Mean Value Theorem

“…b − a Many extension, generalization and forms of MVT were proposed by many mathematicians from all over the worlds. In this article we will discuss Flett's Mean Value Theorem (FMVT) [1] and Extended Generalized Mean Value Theorem (EGMVT) [3]. Then we will state a new form of MVT based on FMVT and EGMVT and we called it Extended Generalized Fleet's Mean Value Theorem (EGFMVT).…”

“…In 2014, Phillip Mafuta [3], stated and proved a theorem of a similar flavor to the Generalized Mean Value Theorem for functions of one variable. For lack of a better term, he called the theorem "Extended Generalized Mean Value Theorem (EGMVT)".…”

“…Theorem 3.1. [3] Let n ∈ N and let f (x), g 1 (x), g 2 (x), g 3 (x), ......, g n (x) be n + 1 continuous functions on a closed bounded interval…”