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ON THE FRACTIONAL MEAN-VALUE THEOREM
International Journal of Bifurcation and Chaos, 2012In this paper, we derive a fractional mean-value theorem both in the sense of Riemann–Liouville and in the sense of Caputo. This new formulation is more general than the generalized Taylor's formula of Kolwankar and the fractional mean-value theorem in the sense of Riemann–Liouville developed by Trujillo.
Guo, Peng, Li, Changpin, Chen, Guanrong
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The American Mathematical Monthly, 1969
(1969). On Mean Value Theorems. The American Mathematical Monthly: Vol. 76, No. 1, pp. 70-73.
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(1969). On Mean Value Theorems. The American Mathematical Monthly: Vol. 76, No. 1, pp. 70-73.
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Quantitative Mean-Value Theorems
1980In the present chapter we obtain two estimates for the average behaviour of a multiplicative function, and pay attention to the error terms involved. Besides being of interest in their own right the results which we shall prove will be applicable to the study of additive functions, both globally in the next chapter, and locally in Chapter 21.
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2014
In this chapter, which is independent of all subsequent chapters, we allow ourselves a brief diversion. We have met and used Rolle’s Theorem (Theorem 5.1), its extension the Mean Value Theorem (Theorem 5.2), and its extension Cauchy’s Mean Value Theorem (Theorem 5.11). Here we consider other Mean Value – type theorems.
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In this chapter, which is independent of all subsequent chapters, we allow ourselves a brief diversion. We have met and used Rolle’s Theorem (Theorem 5.1), its extension the Mean Value Theorem (Theorem 5.2), and its extension Cauchy’s Mean Value Theorem (Theorem 5.11). Here we consider other Mean Value – type theorems.
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2017
This chapter is dedicated entirely to the Mean Value Theorem and its complex history. The opening section offers modern statements of the Mean Value Theorem and some of its variants, proofs of these results, their interrelations, and some applications. The second section provides to some extent the prehistory of the Mean Value Theorem, from Apollonius ...
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This chapter is dedicated entirely to the Mean Value Theorem and its complex history. The opening section offers modern statements of the Mean Value Theorem and some of its variants, proofs of these results, their interrelations, and some applications. The second section provides to some extent the prehistory of the Mean Value Theorem, from Apollonius ...
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Mean-Value Theorem with Small Subdifferentials
Journal of Optimization Theory and Applications, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1986
Giver a curve, y = f(x), we shall use the derivative to give us information about the curve. For instance, we shall find the maximum and minimum of the graph, and regions where the curve is increasing or decreasing. We shall use the mean value theorem, which is basic in the theory of derivatives.
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Giver a curve, y = f(x), we shall use the derivative to give us information about the curve. For instance, we shall find the maximum and minimum of the graph, and regions where the curve is increasing or decreasing. We shall use the mean value theorem, which is basic in the theory of derivatives.
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On a Certain Mean Value Theorem
Moscow University Mathematics Bulletin, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Some weighted quadrature methods based upon the mean value theorems
Mathematical Methods in the Applied Sciences, 2021Herbert H H Homeier +2 more
exaly
2014
The main focus of this chapter is the Mean Value Theorem and some of its applications. This is the big theorem in the world of differentiable functions. Many important results in calculus (and well beyond!) follow from the Mean Value Theorem. We also look at an interesting and useful generalization, due to Cauchy.
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The main focus of this chapter is the Mean Value Theorem and some of its applications. This is the big theorem in the world of differentiable functions. Many important results in calculus (and well beyond!) follow from the Mean Value Theorem. We also look at an interesting and useful generalization, due to Cauchy.
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