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Journal articles on the topic 'Mean value theorems'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 April 2022

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1

Mukhopadhyay, S. N., and S. Ray. "Mean value theorems for divided differences and approximate Peano derivatives." Mathematica Bohemica 134, no. 2 (2009): 165–71. http://dx.doi.org/10.21136/mb.2009.140651.

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2

Ni, Lei. "Mean Value Theorems on Manifolds." Asian Journal of Mathematics 11, no. 2 (2007): 277–304. http://dx.doi.org/10.4310/ajm.2007.v11.n2.a6.

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3

Rassias, Themistocles M., and Young-Ho Kim. "On certain mean value theorems." Mathematical Inequalities & Applications, no. 3 (2008): 431–41. http://dx.doi.org/10.7153/mia-11-32.

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4

Matkowski, Janusz. "Power means generated by some mean-value theorems." Proceedings of the American Mathematical Society 139, no. 10 (October 1, 2011): 3601. http://dx.doi.org/10.1090/s0002-9939-2011-10981-x.

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5

Kôzaki, Masanori. "On mean value theorems for small geodesic spheres in Riemannian manifolds." Czechoslovak Mathematical Journal 42, no. 3 (1992): 519–47. http://dx.doi.org/10.21136/cmj.1992.128352.

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6

Krylov, N. V. "Mean value theorems for stochastic integrals." Annals of Probability 29, no. 1 (February 2001): 385–410. http://dx.doi.org/10.1214/aop/1008956335.

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7

Baker, J. A. "Mean Value Theorems via Spectral Synthesis." Journal of Mathematical Analysis and Applications 193, no. 1 (July 1995): 306–17. http://dx.doi.org/10.1006/jmaa.1995.1237.

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8

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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9

PETER, IOAN RADU, and DORIAN POPA. "Stability of points in mean value theorems." Publicationes Mathematicae Debrecen 83, no. 3 (October 1, 2013): 375–84. http://dx.doi.org/10.5486/pmd.2013.5531.

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10

Huang, Jingjing, and Robert C. Vaughan. "Mean value theorems for binary Egyptian fractions." Journal of Number Theory 131, no. 9 (September 2011): 1641–56. http://dx.doi.org/10.1016/j.jnt.2011.04.001.

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11

Azagra, D., and R. Deville. "Subdifferential Rolle's and mean value inequality theorems." Bulletin of the Australian Mathematical Society 56, no. 2 (October 1997): 319–29. http://dx.doi.org/10.1017/s0004972700031063.

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In this note we give a subdifferential mean value inequality for every continuous Gâteaux subdiferentiable function f in a Banach space which only requires a bound for one but not necessarily all of the subgradients of f at every point of its domain. We also give a subdifferential approximate Rolle's theorem satating that if a subdifferentiable function oscilllates between −ɛ and ɛ on the boundary of the unit ball then there exists a subgradient of the function at an interior point of the ball which has norm less than or equal to 2ɛ.

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12

Fomenko, O. M. "Mean value theorems for automorphic $L$-functions." St. Petersburg Mathematical Journal 19, no. 5 (June 27, 2008): 853–66. http://dx.doi.org/10.1090/s1061-0022-08-01024-8.

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13

SABELFELD, K. K., and I. A. SHALIMOVA. "Mean value theorems in Monte Carlo methods." Russian Journal of Numerical Analysis and Mathematical Modelling 3, no. 3 (1988): 217–30. http://dx.doi.org/10.1515/rnam.1988.3.3.217.

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14

Quinto, Eric Todd. "Mean value extension theorems and microlocal analysis." Proceedings of the American Mathematical Society 131, no. 10 (February 12, 2003): 3267–74. http://dx.doi.org/10.1090/s0002-9939-03-06926-0.

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15

Ash, J. M., and R. L. Jones. "Mean value theorems for generalized Riemann derivatives." Proceedings of the American Mathematical Society 101, no. 2 (February 1, 1987): 263. http://dx.doi.org/10.1090/s0002-9939-1987-0902539-2.

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16

Baker, J. A. "Triangular mean value theorems and Fréchet's equation." Acta Mathematica Hungarica 69, no. 1-2 (March 1995): 111–26. http://dx.doi.org/10.1007/bf01874613.

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17

Bourgain, Jean. "Decoupling inequalities and some mean-value theorems." Journal d'Analyse Mathématique 133, no. 1 (October 2017): 313–34. http://dx.doi.org/10.1007/s11854-017-0035-2.

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18

Volchkov, V. V. "New mean value theorems for polyanalytic functions." Mathematical Notes 56, no. 3 (September 1994): 889–95. http://dx.doi.org/10.1007/bf02362407.

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19

Uçar, Sümeyra, and Nihal Özgür. "Complex conformable Rolle’s and Mean Value Theorems." Mathematical Sciences 14, no. 3 (June 9, 2020): 215–18. http://dx.doi.org/10.1007/s40096-020-00332-x.

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20

Tse, Kung Kuen. "A Note on the Mean Value Theorems." Advances in Pure Mathematics 11, no. 05 (2021): 395–99. http://dx.doi.org/10.4236/apm.2021.115026.

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21

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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22

MATSUMOTO, Kohji, and Hirofumi TSUMURA. "Mean value theorems for the double zeta-function." Journal of the Mathematical Society of Japan 67, no. 1 (January 2015): 383–406. http://dx.doi.org/10.2969/jmsj/06710383.

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23

Gots, E. G., and O. M. Penkin. "Mean-value theorems for Laplacians on stratified sets." Journal of Mathematical Sciences 126, no. 6 (April 2005): 1630–42. http://dx.doi.org/10.1007/s10958-005-0052-z.

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24

Tan, Chengguan, and Songxiao Li. "Some new mean value theorems of Flett type." International Journal of Mathematical Education in Science and Technology 45, no. 7 (April 10, 2014): 1103–7. http://dx.doi.org/10.1080/0020739x.2014.904527.

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25

GAJEK and ZAGRODNY. "Geometric Mean Value Theorems for the Dini Derivative." Journal of Mathematical Analysis and Applications 191, no. 1 (April 1, 1995): 56–76. http://dx.doi.org/10.1016/s0022-247x(85)71120-1.

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26

Huang, Jing-Jing, and Robert C. Vaughan. "Mean value theorems for binary Egyptian fractions II." Acta Arithmetica 155, no. 3 (2012): 287–96. http://dx.doi.org/10.4064/aa155-3-5.

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27

Gajek, L., and D. Zagrodny. "Geometric Mean Value Theorems for the Dini Derivative." Journal of Mathematical Analysis and Applications 191, no. 1 (April 1995): 56–76. http://dx.doi.org/10.1006/jmaa.1995.1120.

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28

Mercer, Peter R. "Type, fixed point iteration, and mean value theorems." International Journal of Mathematical Education in Science and Technology 32, no. 2 (March 2001): 308–12. http://dx.doi.org/10.1080/002073901300037843.

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29

Tiryaki, Aydin, and Devrim Çakmak. "Sahoo- and Wayment-type integral mean value theorems." International Journal of Mathematical Education in Science and Technology 41, no. 4 (June 15, 2010): 565–73. http://dx.doi.org/10.1080/00207390903564678.

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30

Volchkov, V. V. "Mean value theorems for a class of polynomials." Siberian Mathematical Journal 35, no. 4 (July 1994): 656–63. http://dx.doi.org/10.1007/bf02106608.

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31

Polovinkin, I. P. "Mean Value Theorems for Linear Partial Differential Equations." Journal of Mathematical Sciences 197, no. 3 (February 1, 2014): 399–403. http://dx.doi.org/10.1007/s10958-014-1721-6.

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32

Martínez, Francisco, Inmaculada Martínez, Mohammed K. A. Kaabar, and Silvestre Paredes. "Generalized Conformable Mean Value Theorems with Applications to Multivariable Calculus." Journal of Mathematics 2021 (April 1, 2021): 1–7. http://dx.doi.org/10.1155/2021/5528537.

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The conformable derivative and its properties have been recently introduced. In this research work, we propose and prove some new results on the conformable calculus. By using the definitions and results on conformable derivatives of higher order, we generalize the theorems of the mean value which follow the same argument as in the classical calculus. The value of conformable Taylor remainder is obtained through the generalized conformable theorem of the mean value. Finally, we introduce the conformable version of two interesting results of classical multivariable calculus via the conformable formula of finite increments.

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33

BRAKER, U. S., and D. S. HOODA. "MEAN VALUE CHARACTERIZATION OF 'USEFUL' INFORMATION MEASURES." Tamkang Journal of Mathematics 24, no. 4 (December 1, 1993): 383–94. http://dx.doi.org/10.5556/j.tkjm.24.1993.4510.

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In the present communication the generalized mean value characterization of 'useful' information and relativeinformation measures has been studied. Some comparison theorems related to these measures have also been proved.

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34

Bullen, P. S., and D. N. Sarkhel. "On Darboux and Mean Value Properties." Canadian Mathematical Bulletin 30, no. 2 (June 1, 1987): 223–30. http://dx.doi.org/10.4153/cmb-1987-032-8.

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AbstractIn this paper we extend and greatly generalize, with some new information, the well known results that an approximately continuous function is Darboux, and that a finite approximate derivative has the mean value property and is Darboux. Our theorems on Darboux and mean value properties of derivatives include also those of selective derivatives and I-approximate derivatives.

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35

Hildebrand, Adolf. "Quantitative mean value theorems for nonnegative multiplicative functions II." Acta Arithmetica 48, no. 3 (1987): 209–60. http://dx.doi.org/10.4064/aa-48-3-209-260.

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36

Pratsiovytyi, Mykola, and Vitaliy Drozdenko. "Characterization theorems for mean value insurance premium calculation principle." Tbilisi Mathematical Journal 6 (2013): 57–71. http://dx.doi.org/10.32513/tbilisi/1528768937.

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37

Kumar, Satish, Gurdas Ram, and Vishal Gupta. "Some Coding Theorems for Nonadditive Generalized Mean-Value Entropies." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/315686.

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38

Chen, Wei, and Dandan Li. "Some uncertain differential mean value theorems and stability analysis." Journal of Intelligent & Fuzzy Systems 34, no. 4 (April 19, 2018): 2343–50. http://dx.doi.org/10.3233/jifs-171399.

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39

Topal, S. Gulsan. "Rolle's and Generalized Mean Value Theorems on Time Scales." Journal of Difference Equations and Applications 8, no. 4 (January 2002): 333–44. http://dx.doi.org/10.1080/102619029001.

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40

Matsumoto, Kohji. "Liftings and mean value theorems for automorphic L-functions." Proceedings of the London Mathematical Society 90, no. 02 (February 25, 2005): 297–320. http://dx.doi.org/10.1112/s0024611504015096.

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41

Ngô, Quô´c-Anh. "Some mean value theorems for integrals on time scales." Applied Mathematics and Computation 213, no. 2 (July 2009): 322–28. http://dx.doi.org/10.1016/j.amc.2009.03.025.

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42

Fomeriko, O. M. "Mean value theorems for a class of Dirichlet series." Journal of Mathematical Sciences 157, no. 4 (February 18, 2009): 659–73. http://dx.doi.org/10.1007/s10958-009-9335-0.

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43

Pečarić, Josip E., Ivan Perić, and H. M. Srivastava. "A family of the Cauchy type mean-value theorems." Journal of Mathematical Analysis and Applications 306, no. 2 (June 2005): 730–39. http://dx.doi.org/10.1016/j.jmaa.2004.10.018.

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44

Basrak, Bojan. "Limit Theorems for the Inductive Mean on Metric Trees." Journal of Applied Probability 47, no. 04 (December 2010): 1136–49. http://dx.doi.org/10.1017/s0021900200007427.

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For random variables with values on binary metric trees, the definition of the expected value can be generalized to the notion of a barycenter. To estimate the barycenter from tree-valued data, the so-called inductive mean is constructed recursively using the weighted interpolation between the current mean and a new data point. We show the strong consistency of the inductive mean, but also that it, somewhat peculiarly, converges towards the true barycenter with different rates, and asymptotic distributions depending on the small variations of the underlying distribution.

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45

Basrak, Bojan. "Limit Theorems for the Inductive Mean on Metric Trees." Journal of Applied Probability 47, no. 4 (December 2010): 1136–49. http://dx.doi.org/10.1239/jap/1294170525.

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For random variables with values on binary metric trees, the definition of the expected value can be generalized to the notion of a barycenter. To estimate the barycenter from tree-valued data, the so-called inductive mean is constructed recursively using the weighted interpolation between the current mean and a new data point. We show the strong consistency of the inductive mean, but also that it, somewhat peculiarly, converges towards the true barycenter with different rates, and asymptotic distributions depending on the small variations of the underlying distribution.

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46

Zhang, Wen-Bin. "Mean-value theorems and extensions of the Elliott-Daboussi theorem on additive arithmetic semigroups." Ramanujan Journal 15, no. 1 (December 18, 2007): 47–75. http://dx.doi.org/10.1007/s11139-007-9115-8.

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47

Kolahdouz, Fahimeh, Farzad Radmehr, and Hassan Alamolhodaei. "Exploring students’ proof comprehension of the Cauchy Generalized Mean Value Theorem." Teaching Mathematics and its Applications: An International Journal of the IMA 39, no. 3 (December 23, 2019): 213–35. http://dx.doi.org/10.1093/teamat/hrz016.

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Abstract Undergraduate students majoring in mathematics often face difficulties in comprehending mathematical proofs. Inspired by a number of studies related to students’ proof comprehension, and Mejia-Ramos et al.’s study in particular, a test was designed in relation to the proof comprehension of the Cauchy Generalized Mean Value Theorem (CGMVT). The test mainly focused on (a.) investigating students’ understanding of relations between the statements within the CGMVT proof and (b.) the relations between the CGMVT and other theorems. Thirty-five first-year university students voluntarily participated in this study. In addition, 10 of these students were subsequently interviewed to seek their opinion about the test. Test results indicated that most of the students lacked an understanding of the relations between the mathematical statements within the CGMVT proof, and the relations between the CGMVT and other theorems. The results of interviews showed that this type of assessment was new to students and helped them to improve their insights into mathematical proofs. The findings suggested such a test design could be used more frequently in assessments to aid instructors’ understanding of students’ proof comprehension and to teach students how mathematical proofs should be learned.

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48

Trif, Tiberiu. "Asymptotic behavior of intermediate points in certain mean value theorems." Journal of Mathematical Inequalities, no. 2 (2008): 151–61. http://dx.doi.org/10.7153/jmi-02-15.

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49

Marinescu, Dan Ştefan, and Mihai Monea. "Some mean value theorems as consequences of the Darboux property." Mathematica Bohemica 142, no. 2 (December 16, 2016): 211–24. http://dx.doi.org/10.21136/mb.2016.0032-15.

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50

Berenstein, Carlos, and Daniel Pascuas. "Morera and mean-value type theorems in the hyperbolic disk." Israel Journal of Mathematics 86, no. 1-3 (October 1994): 61–106. http://dx.doi.org/10.1007/bf02773674.

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