2014
DOI: 10.1007/s00010-014-0311-5
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On Flett’s mean value theorem

Abstract: Abstract. This paper reviews the current state of the art of the mean value theorem due to Thomas M. Flett. We present the results with detailed proofs and provide many new proofs of known results. Moreover, some new observations and yet unpublished results are included.

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Cited by 7 publications
(5 citation statements)
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“…More exactly, we show that all the improved results (previously proved in case of functions of class C 2 ) hold true even in the case of continuous functions (Theorems 4,6,13,14), in the case of continuously differentiable functions (Theorems 7,8), or in the case of one time differentiable functions (Theorems 5,9,10).…”
Section: The Resultsmentioning
confidence: 77%
See 1 more Smart Citation
“…More exactly, we show that all the improved results (previously proved in case of functions of class C 2 ) hold true even in the case of continuous functions (Theorems 4,6,13,14), in the case of continuously differentiable functions (Theorems 7,8), or in the case of one time differentiable functions (Theorems 5,9,10).…”
Section: The Resultsmentioning
confidence: 77%
“…Proof of Theorem 6 We assume without loss of generality that f is strictly concave on [a, c] and strictly convex on [c, b]. The following relations hold true for every arbitrarily fixed u, v ∈ (c − ε, c) ∩ (a, b), u < v and w, z ∈ (c, c + ε) ∩ (a, b), w < z:…”
Section: Proof Of Theoremmentioning
confidence: 97%
“…In this paper, the main method we concern to discuss for estimating the RNF is through the mean value theorem for integral method. Some literature discuss the basic theory and application of the mean value theorem for integral method such as Merikoski et al (2009), Mihai (2015), and Hutník & Molnárová (2015). The application of the mean value theorem for integral in the warranty modeling have been used for estimating 1D RNIE in the Maghsoodloo & Helvaci (2014) and Sasongko & Mahatma (2016).…”
Section: B Methodsmentioning
confidence: 99%
“…3.To see which geometrical consequences do such result have? [2]. Notations: Throughout in this article we will use following notations.…”
Section: Flett's Mean Value Theoremmentioning
confidence: 99%
“…Example 2.3. [2] In which point of curve y = x 3 the tangent passes through the point X = [−2, 2]? Solution -To verify X lies on curve and y = x 2 differentiable on R. Since…”
Section: Flett's Mean Value Theoremmentioning
confidence: 99%