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Journal articles on the topic 'Mean Value Theorem'

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1

Matkowski, Janusz. "Mean-value theorem for vector-valued functions." Mathematica Bohemica 137, no. 4 (2012): 415–23. http://dx.doi.org/10.21136/mb.2012.142997.

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2

Trokhimchuk, Yu Yu. "Mean-Value Theorem." Ukrainian Mathematical Journal 65, no. 9 (February 2014): 1418–25. http://dx.doi.org/10.1007/s11253-014-0869-z.

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3

Merikoski, Jorma K., Markku Halmetoja, and Timo Tossavainen. "Means and the mean value theorem." International Journal of Mathematical Education in Science and Technology 40, no. 6 (September 15, 2009): 729–40. http://dx.doi.org/10.1080/00207390902825328.

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4

Tokieda, Tadashi F. "A Mean Value Theorem." American Mathematical Monthly 106, no. 7 (August 1999): 673. http://dx.doi.org/10.2307/2589498.

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5

Tokieda, Tadashi F. "A Mean Value Theorem." American Mathematical Monthly 106, no. 7 (August 1999): 673–74. http://dx.doi.org/10.1080/00029890.1999.12005102.

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6

PALES, ZSOLT. "A general mean value theorem." Publicationes Mathematicae Debrecen 89, no. 1-2 (July 1, 2016): 161–72. http://dx.doi.org/10.5486/pmd.2016.7443.

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7

de Camargo, André Pierro. "The geometric Mean Value Theorem." International Journal of Mathematical Education in Science and Technology 49, no. 4 (November 8, 2017): 613–15. http://dx.doi.org/10.1080/0020739x.2017.1394503.

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8

Trokhimchuk, Yurii Yu. "To the mean-value theorem." Journal of Mathematical Sciences 188, no. 2 (December 15, 2012): 128–45. http://dx.doi.org/10.1007/s10958-012-1112-9.

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9

Penot, J. P. "On the mean value theorem." Optimization 19, no. 2 (January 1988): 147–56. http://dx.doi.org/10.1080/02331938808843330.

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10

Mercer, Peter R. "On A Mean Value Theorem." College Mathematics Journal 33, no. 1 (January 2002): 46. http://dx.doi.org/10.2307/1558980.

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11

Kim, Sung Soo, and John Holbrook. "A Very Mean Value Theorem." Mathematical Intelligencer 25, no. 1 (December 2003): 42–47. http://dx.doi.org/10.1007/bf02985637.

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12

Wooley, Trevor D. "On Vinogradov's mean value theorem." Mathematika 39, no. 2 (December 1992): 379–99. http://dx.doi.org/10.1112/s0025579300015102.

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13

Tong, Jingcheng. "On Flett's mean value theorem." International Journal of Mathematical Education in Science and Technology 35, no. 6 (November 2004): 936–41. http://dx.doi.org/10.1080/00207390412331271339.

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14

Sand, Mark. "MEAN VALUE THEOREM NO MORE!!" PRIMUS 5, no. 4 (January 1995): 339–42. http://dx.doi.org/10.1080/10511979508965798.

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15

Hutník, Ondrej, and Jana Molnárová. "On Flett’s mean value theorem." Aequationes mathematicae 89, no. 4 (October 22, 2014): 1133–65. http://dx.doi.org/10.1007/s00010-014-0311-5.

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16

de Reyna, Juan Arias. "A generalized mean-value theorem." Monatshefte für Mathematik 106, no. 2 (June 1988): 95–97. http://dx.doi.org/10.1007/bf01298830.

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17

Hardin, Christopher S., and Daniel J. Velleman. "The mean value theorem in second order arithmetic." Journal of Symbolic Logic 66, no. 3 (September 2001): 1353–58. http://dx.doi.org/10.2307/2695111.

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This paper is a contribution to the project of determining which set existence axioms are needed to prove various theorems of analysis. For more on this project and its history we refer the reader to [1] and [2].We work in a weak subsystem of second order arithmetic. The language of second order arithmetic includes the symbols 0, 1, =, <, +, ·, and ∈, together with number variables x, y, z, … (which are intended to stand for natural numbers), set variables X, Y, Z, … (which are intended to stand for sets of natural numbers), and the usual quantifiers (which can be applied to both kinds of variables) and logical connectives. We write ∀x < t φ and ∃x < t φ as abbreviations for ∀x(x < t → φ) and ∃x{x < t ∧ φ) respectively; these are called bounded quantifiers. A formula is said to be if it has no quantifiers applied to set variables, and all quantifiers applied to number variables are bounded. It is if it has the form ∃xθ and it is if it has the form ∀xθ, where in both cases θ is .The theory RCA0 has as axioms the usual Peano axioms, with the induction scheme restricted to formulas, and in addition the comprehension scheme, which consists of all formulas of the formwhere φ is , ψ is , and X does not occur free in φ(n). (“RCA” stands for “Recursive Comprehension Axiom.” The reason for the name is that the comprehension scheme is only strong enough to prove the existence of recursive sets.) It is known that this theory is strong enough to allow the development of many of the basic properties of the real numbers, but that certain theorems of elementary analysis are not provable in this theory. Most relevant for our purposes is the fact that it is impossible to prove in RCA0 that every continuous function on the closed interval [0, 1] attains maximum and minimum values (see [1]).Since the most common proof of the Mean Value Theorem makes use of this theorem, it might be thought that the Mean Value Theorem would also not be provable in RCA0. However, we show in this paper that the Mean Value Theorem can be proven in RCA0. All theorems stated in this paper are theorems of RCA0, and all of our reasoning will take place in RCA0.
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18

Matkowski, Janusz, and Iwona Pawlikowska. "Homogeneous means generated by a mean-value theorem." Journal of Mathematical Inequalities, no. 4 (2010): 467–79. http://dx.doi.org/10.7153/jmi-04-43.

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19

Koliha, J. J. "Mean, Meaner, and the Meanest Mean Value Theorem." American Mathematical Monthly 116, no. 4 (April 2009): 356–61. http://dx.doi.org/10.1080/00029890.2009.11920948.

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20

Koliha, J. J. "Mean, Meaner, and the Meanest Mean Value Theorem." American Mathematical Monthly 116, no. 4 (April 1, 2009): 356–61. http://dx.doi.org/10.4169/193009709x470227.

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21

Bailey, D. F., and G. J. Fix. "A generalization of the mean mean value theorem." Applied Mathematics Letters 1, no. 4 (1988): 327–30. http://dx.doi.org/10.1016/0893-9659(88)90143-7.

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22

Molnárová, Jana. "On Generalized Flett's Mean Value Theorem." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/574634.

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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.
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23

Berrone, L. R., and J. Moro. "On means generated through the Cauchy mean value theorem." Aequationes mathematicae 60, no. 1-2 (August 2000): 1–14. http://dx.doi.org/10.1007/s000100050131.

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24

GUO, PENG, CHANGPIN LI, and GUANRONG CHEN. "ON THE FRACTIONAL MEAN-VALUE THEOREM." International Journal of Bifurcation and Chaos 22, no. 05 (May 2012): 1250104. http://dx.doi.org/10.1142/s0218127412501040.

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In 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.
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25

Chubarikov, V. N. "On a Certain Mean Value Theorem." Moscow University Mathematics Bulletin 74, no. 1 (January 2019): 35–37. http://dx.doi.org/10.3103/s0027132219010078.

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26

Chen, Zhibing, and Shusen Ding. "A Higher Mean Value Theorem: 10935." American Mathematical Monthly 110, no. 6 (June 2003): 544. http://dx.doi.org/10.2307/3647923.

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27

Wooley, Trevor D. "On Vinogradov's mean value theorem. II." Michigan Mathematical Journal 40, no. 1 (1993): 175–80. http://dx.doi.org/10.1307/mmj/1029004681.

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28

Penot, J. P. "Mean-Value Theorem with Small Subdifferentials." Journal of Optimization Theory and Applications 94, no. 1 (July 1997): 209–21. http://dx.doi.org/10.1023/a:1022672005994.

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29

Wooley, Trevor D. "Corrigendum: On Vinogradov's mean value theorem." Mathematika 40, no. 1 (June 1993): 152. http://dx.doi.org/10.1112/s0025579300013796.

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30

Barbut, Erol, and Gene Denzel. "Meandering around the mean value theorem." International Journal of Mathematical Education in Science and Technology 19, no. 1 (January 1988): 139–43. http://dx.doi.org/10.1080/0020739880190118.

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31

Nikonorov, Yu G. "On the integral mean value theorem." Siberian Mathematical Journal 34, no. 6 (1993): 1135–37. http://dx.doi.org/10.1007/bf00973476.

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32

Mercer, Peter R. "101.07 Cauchy's mean value theorem meets the logarithmic mean." Mathematical Gazette 101, no. 550 (February 3, 2017): 108–15. http://dx.doi.org/10.1017/mag.2017.15.

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33

de Camargo, André Pierro. "A New Proof of the Equivalence of the Cauchy Mean Value Theorem and the Mean Value Theorem." American Mathematical Monthly 127, no. 5 (April 23, 2020): 460. http://dx.doi.org/10.1080/00029890.2020.1722552.

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34

Mitrea, Dorina, and Heather Rosenblatt. "A general converse theorem for mean-value theorems in linear elasticity." Mathematical Methods in the Applied Sciences 29, no. 12 (2006): 1349–61. http://dx.doi.org/10.1002/mma.725.

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35

Tong, Jingcheng. "Cauchy's Mean Value Theorem Involving n Functions." College Mathematics Journal 35, no. 1 (January 2004): 50. http://dx.doi.org/10.2307/4146885.

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36

Kupka, Ivan. "Topological generalization of Cauchy's mean value theorem." Annales Academiae Scientiarum Fennicae Mathematica 41 (February 2016): 315–20. http://dx.doi.org/10.5186/aasfm.2016.4120.

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37

Fejzic, H., and D. Rinne. "More on a Mean Value Theorem Converse." American Mathematical Monthly 106, no. 5 (May 1999): 454. http://dx.doi.org/10.2307/2589151.

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38

Wooley, Trevor. "Vinogradov's mean value theorem via efficient congruencing." Annals of Mathematics 175, no. 3 (May 1, 2012): 1575–627. http://dx.doi.org/10.4007/annals.2012.175.3.12.

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39

Schaumberger, Norman. "More Applications of the Mean Value Theorem." College Mathematics Journal 16, no. 5 (November 1985): 397. http://dx.doi.org/10.2307/2687000.

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40

Lozada-Cruz, German. "Some variants of Lagrange's mean value theorem." Selecciones Matemáticas 7, no. 1 (June 30, 2020): 144–50. http://dx.doi.org/10.17268/sel.mat.2020.01.13.

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41

Vaughan, R. C. "A mean value theorem for cubic fields." Journal of Number Theory 100, no. 1 (May 2003): 169–83. http://dx.doi.org/10.1016/s0022-314x(02)00075-6.

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42

Matkowski, Janusz. "A mean-value theorem and its applications." Journal of Mathematical Analysis and Applications 373, no. 1 (January 2011): 227–34. http://dx.doi.org/10.1016/j.jmaa.2010.06.057.

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43

Davitt, R. M., R. C. Powers, T. Riedel, and P. K. Sahoo. "Flett's Mean Value Theorem for Holomorphic Functions." Mathematics Magazine 72, no. 4 (October 1, 1999): 304. http://dx.doi.org/10.2307/2691225.

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44

Soleimani-damaneh, M. "A mean value theorem in Asplund spaces." Nonlinear Analysis: Theory, Methods & Applications 68, no. 10 (May 2008): 3103–6. http://dx.doi.org/10.1016/j.na.2007.03.002.

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45

Lozada-Cruz, German. "Some variants of Cauchy's mean value theorem." International Journal of Mathematical Education in Science and Technology 51, no. 7 (December 23, 2019): 1155–63. http://dx.doi.org/10.1080/0020739x.2019.1703150.

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46

Tong, Jingcheng, and Peter A. Braza. "A Converse of the Mean Value Theorem." American Mathematical Monthly 104, no. 10 (December 1997): 939–42. http://dx.doi.org/10.1080/00029890.1997.11990743.

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47

Fejzić, H., and D. Rinne. "More on a Mean Value Theorem Converse." American Mathematical Monthly 106, no. 5 (May 1999): 454–55. http://dx.doi.org/10.1080/00029890.1999.12005069.

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48

Schaumberger, Norman. "More Applications of the Mean Value Theorem." College Mathematics Journal 16, no. 5 (November 1985): 397–98. http://dx.doi.org/10.1080/07468342.1985.11972914.

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49

Muldowney, James S. "The Converse of Pólya’s Mean Value Theorem." SIAM Journal on Mathematical Analysis 18, no. 5 (September 1987): 1317–22. http://dx.doi.org/10.1137/0518095.

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50

Kozlov, V. V. "Cauchy's mean value theorem and continued fractions." Russian Mathematical Surveys 72, no. 1 (February 28, 2017): 182–84. http://dx.doi.org/10.1070/rm9757.

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