Bibliography for the Mean Value Theorem

unabridged

  1. Type, fixed point iteration, and mean value theorems  
    Mercer, Peter R.  
    Internat. J. Math. Ed. Sci. Tech. 32 (2001), no. 2, 308--312, Math. Sci. Net.  
  2. Inverse proposition of mean value theorem of double integral  
    Hao, J.-l.; Liu, J.-q.  
    Journal- Shangqiu Teachers College, 2001, vol. 17, no. 2, pp. 109-111, Ingenta.  
  3. The mean value theorem of Lagrange generalised to involve two functions  
    Tong, J.  
    Mathematical Gazette, 2000, vol. 84, no. 501, pp. 515, Ingenta.  
  4. Polya's Lagrange mean value theorem. (Chinese)  
    Han, Ying
    J. Liaoning Norm. Univ. Nat. Sci. 23 (2000), no. 4, 353--355, Math. Sci. Net.  
  5. Une variante du théorème de Cauchy de la valeur moyenne. (French) [A variant of the Cauchy mean value theorem]
    Wachnicki, Eugeniusz
    Demonstratio Math. 33 (2000), no. 4, 737--740, Math. Sci. Net.  
  6. The mean value theorems of Lagrange and Cauchy. II  
    Tong, Jingcheng
    Internat. J. Math. Ed. Sci. Tech. 31 (2000), no. 3, 447--449, Math. Sci. Net.  
  7. On means generated through the Cauchy mean value theorem.
    Berrone, Lucio R.; Moro, Julio
    Aequationes Math. 60 (2000), no. 1-2, 1--14, Math. Sci. Net.  
  8. A constructive converse of the mean value theorem.
    Spitters, Bas; Veldman, Wim
    Indag. Math. (N.S.) 11 (2000), no. 1, 151--157, Math. Sci. Net.  
  9. A probabilistic analogue of the mean value theorem and its applications to reliability theory.  
    Di Crescenzo, Antonio  
    Journal of applied probability, 1999, vol. 36, no. 3, pp. 706, Ingenta.  
  10. A note on the Cauchy mean value theorem. (Chinese)
    Tao, Xu Heng; Fan, Ji Shan
    J. Southeast Univ. 29 (1999), no. 5, 74--75, Math. Sci. Net.  
  11. Likely mean value theorem for the integral of fuzzy mapping between fuzzy bounds.
    Lee, Bu-Young; Park, Dong-Gun; Kwun, Young-Chel
    Far East J. Math. Sci. (FJMS) 1 (1999), no. 3, 455--463, Math. Sci. Net.  
  12. A Mean Value Theorem  
    Tokieda, Tadashi F.  
    The american mathematical monthly, 1999, vol. 106, no. 7, pp. 673, Ingenta.   
  13. More on a mean value theorem converse  
    Fejzi, H.; Rinne, D.  
    Amer. Math. Monthly 106 (1999), no. 5, 454--455, Math. Sci. Net.  
  14. A physically motivated further note on the mean value theorem for integrals  
    Schwind, William J.; Ji, Jun; Koditschek, Daniel E.  
    Amer. Math. Monthly 106 (1999), no. 6, 559--564, Math. Sci. Net.  
  15. The mean value theorems of Lagrange and Cauchy  
    Tong, Jingcheng  
    Internat. J. Math. Ed. Sci. Tech. 30 (1999), no. 3, 456--458, Math. Sci. Net.  
  16. A note on the mean value theorem.
    Hikida, Masato
    Math. Japon. 50 (1999), no. 2, 161--167, Math. Sci. Net.  
  17. Mean value theorem for complex analytic functions.
    Li, Ying
    Natur. Sci. J. Xiangtan Univ. 21 (1999), no. 4, 125--129, Math. Sci. Net.  
  18. Flett's mean value theorem for holomorphic functions  
    Davitt, R. M.; Powers, R. C.; Riedel, T.; Sahoo, P. K.
    Math. Mag. 72 (1999), no. 4, 304--307, Math. Sci. Net.  
  19. A Mean value theorem for real continuous functions.
    Crînganu, Jenic
    An. Univ. Bucure sti Mat. 47 (1998), no. 1, 41--44, Math. Sci. Net.  
  20. A converse of the mean value theorem  
    Tong, Jingcheng; Braza, Peter A.  
    Amer. Math. Monthly 104 (1997), no. 10, 939--942, Math. Sci. Net.  
  21. A note on the mean value theorem for integrals  
    Zhang, Bao-lin  
    Amer. Math. Monthly 104 (1997), no. 6, 561--562, Math. Sci. Net.  
  22. Rethinking rigor in calculus: the role of the mean value theorem  
    Tucker, Thomas W.  
    Amer. Math. Monthly 104 (1997), no. 3, 231--240, Math. Sci. Net.  
  23. On certain applications of Cauchy's mean value theorem.
    Pop, Maria S.; Sándor, J.
    Octogon Math. Mag. 4 (1996), no. 2, 23--28, Math. Sci. Net.  
  24. A generalization of the Lagrange mean value theorem.
    Finta, Béla
    Octogon Math. Mag. 4 (1996), no. 2, 38--40, Math. Sci. Net.  
  25. The A strong mean value theorem and applications.
    Luc, Dinh
    Nonlinear Anal. 26 (1996), no. 5, 915--923, Math. Sci. Net.  
  26. A Cauchy's mean value theorem for complex functions  
    Száz, Árpád
    Math. Student 64 (1995), no. 1-4, 125--127 (1996), Math. Sci. Net.  
  27. A note on the generalized mean value theorem. (Chinese)
    Zhang, Shu Yi
    J. Baoji College Arts Sci. Nat. Sci. 1995, no. 2, 75--76, Math. Sci. Net.  
  28. Triangular mean value theorems and Fréchet's equation.
    Baker, J. A.
    Acta Math. Hungar. 69 (1995), no. 1-2, 111--126, Math. Sci. Net.  
  29. Some statistical mean value theorems related to the bootstrap.
    Chao, M. T.; Lo, S. H.
    Statist. Sinica 5 (1995), no. 1, 129--139, Math. Sci. Net.  
  30. A note on the Zagrodny mean value theorem.
    Thibault, L.
    Optimization 35 (1995), no. 2, 127--130, Math. Sci. Net.  
  31. Mean value theorems via division methods.
    Banta s, Gheorghe; Turinici, Mihai
    An. Stiin t. Univ. Al. I. Cuza Ia si Sec t. I a Mat. 40 (1994), no. 2, 135--150, Math. Sci. Net.  
  32. Mean-value theorems for a class of polynomials. (Russian)
    Volchkov, V. V.
    Sibirsk. Mat. Zh. 35 (1994), no. 4, 737--745, i; translation in Siberian Math. J. 35 (1994), no. 4, 656--663, Math. Sci. Net.  
  33. A mean-value theorem for Chebyshev functions. (Russian)
    Rakhmonov, Z. Kh.
    Izv. Ross. Akad. Nauk Ser. Mat. 58 (1994), no. 3, 127--139; translation in Russian Acad. Sci. Izv. Math. 44 (1995), no. 3, 555--569, Math. Sci. Net.  
  34. On sharp estimates in the first mean-value theorem. (Russian)
    Nikonorov, Yu. G.
    Dokl. Akad. Nauk 336 (1994), no. 2, 168--170; translation in Russian Acad. Sci. Dokl. Math. 49 (1994), no. 3, 493--496, Math. Sci. Net.  
  35. Asymptotic properties of the mean value points in mean value theorems.(Chinese)
    Abdukerim, Haji
    J. Xinjiang Univ. Natur. Sci. 11 (1994), no. 1, 39--41, Math. Sci. Net.  
  36. Mean value theorems of inequality form.
    Banta s, Gh.; Turinici, M.
    Mathematica (Cluj) 35(58) (1993), no. 1, 9--13, Math. Sci. Net.  
  37. A note on generalized mean value theorem.
    Zeqing, Liu
    Menemui Mat. 15 (1993), no. 1, 13--15, Math. Sci. Net.  
  38. On the integral mean-value theorem. (Russian)
    Nikonorov, Yu. G.
    Sibirsk. Mat. Zh. 34 (1993), no. 6, 150--152, iii, ix; translation in Siberian Math. J. 34 (1993), no. 6, 1135--1137, Math. Sci. Net.  
  39. A converse to the mean value theorem for harmonic functions.
    Hansen, Wolfhard; Nadirashvili, Nikolai
    Acta Math. 171 (1993), no. 2, 139--163, Math. Sci. Net.  
  40. On Vinogradov's mean value theorem.
    Wooley, Trevor D.
    Mathematika 39 (1992), no. 2, 379--399, Math. Sci. Net.  
  41. On the Mean Value Theorem, Inequality, and Inclusion (in The Teaching of Mathematics)  
    M. Furi, M. Martelli  
    American Mathematical Monthly, Vol. 98, No. 9. (Nov., 1991), pp. 840-846, Jstor.  
  42. A Topological Mean Value Theorem for the Plane (in The Teaching of Mathematics)  
    Ira Rosenholtz  
    American Mathematical Monthly, Vol. 98, No. 2. (Feb., 1991), pp. 149-154, Jstor.  
  43. Some Remarks on the Stability of a Property Related to the Mean Value Theorem for Harmonic Functions  
    Burton Randol  
    Proceedings of the American Mathematical Society, Vol. 114, No. 1. (Jan., 1992), pp. 175-179, Jstor.  
  44. A generalized mean value theorem.
    Yagi, Akiko
    Bull. Yamagata Univ. Natur. Sci. 12 (1991), no. 4, 319--328, Math. Sci. Net.  
  45. More Applications of the Mean Value Theorem  
    Schaumberger, Norman  
    Pi mu epsilon journal, 1990, vol. 9, no. 2, pp. 113, Ingenta.  
  46. Errata, addenda: On the Mean Value Theorem for Integrals (in Notes)  
    American Mathematical Monthly, Vol. 97, No. 5. (May, 1990), p. 412, Jstor.  
  47. Some new applications of the mean value theorem. (Chinese)
    Zhang, Ming Yao
    J. China Univ. Sci. Tech. 19 (1989), no. 1, 38--50, Math. Sci. Net.  
  48. Some applications of the mean value theorem.
    Vojtá sek, Stanislav
    Acta Tech. CSAV 34 (1989), no. 2, 136--143, Math. Sci. Net.  
  49. A generalization of the mean mean value theorem.
    Bailey, D. F.; Fix, G. J.
    Appl. Math. Lett. 1 (1988), no. 4, 327--330, Math. Sci. Net.  
  50. A note on the mean value theorem in differential calculus. (Chinese)
    Zhang, Guang Fan
    Math. Practice Theory 1988, no. 1, 87--89, Math. Sci. Net.  
  51. A generalized mean-value theorem. Monatsh.
    Arias de Reyna, Juan
    Math. 106 (1988), no. 2, 95--97, Math. Sci. Net.  
  52. A numerical method based on the mean value theorem. (Chinese)
    Wu, Ji Ke; Li, Hui
    Math. Numer. Sinica 10 (1988), no. 1, 94--99, Math. Sci. Net.  
  53. On the mean value theorem.
    Penot, J.-P.
    Optimization 19 (1988), no. 2, 147--156, Math. Sci. Net.  
  54. A generalization of the mean value theorem. (Chinese)
    Xu, Mei Hua
    Qufu Shifan Daxue Xuebao Ziran Kexue Ban 13 (1987), no. 3, 217--224, Math. Sci. Net.  
  55. Mean value theorems for generalized Riemann derivatives.
    Ash, J. M.; Jones, R. L.
    Proc. Amer. Math. Soc. 101 (1987), no. 2, 263--271, Math. Sci. Net.  
  56. The converse of Pólya's mean value theorem.
    Muldowney, James S.
    SIAM J. Math. Anal. 18 (1987), no. 5, 1317--1322, Math. Sci. Net.  
  57. On the mean value theorem for analytic functions.
    Gevirtz, Julian
    Michigan Math. J. 33 (1986), no. 3, 365--375, Math. Sci. Net.  
  58. On a mean value theorem in the theory of elasticity. (Chinese)
    Wang, Wei
    Beijing Daxue Xuebao 1986, no. 1, 87--90, Math. Sci. Net.  
  59. A Lattice Summation Using the Mean Value Theorem for Harmonic Functions (in Classroom Notes in Applied Mathematics)  
    Paul K. Mazaika  
    SIAM Review, Vol. 26, No. 1. (Jan., 1984), pp. 113-115, Jstor.  
  60. The mean value theorem and analytic functions.
    Johnston, Elgin H.
    Proc. Edinburgh Math. Soc. (2) 26 (1983), no. 3, 289--295, Math. Sci. Net.  
  61. Errata: "On the mean value theorem for integrals"  
    Wong, Jingcheng  
    [Amer. Math. Monthly 89 (1982), no. 5, 300--301; MR 83g:26002] by B. Jacobson. Amer. Math. Monthly 97 (1990), no. 5, 412, Math. Sci. Net.  
  62. On the Mean Value Theorem for Integrals (in Notes)  
    Bernard Jacobson
    American Mathematical Monthly, Vol. 89, No. 5. (May, 1982), pp. 300-301, Jstor.  
  63. Generalizing the Generalized Mean-Value Theorem (in Classroom Notes)  
    Alexander Abian  
    American Mathematical Monthly, Vol. 88, No. 7. (Aug. - Sep., 1981), pp. 528-530, Jstor.  
  64. Mean value theorems and a Taylor theorem for vector valued functions.
    V'yborn'y, Rudolf
    Bull. Austral. Math. Soc. 24 (1981), no. 1, 69--77, Math. Sci. Net.  
  65. A Strong Converse to Gauss's Mean-Value Theorem (in Classroom Notes)  
    R. B. Burckel  
    American Mathematical Monthly, Vol. 87, No. 10. (Dec., 1980), pp. 819-820, Jstor.  
  66. A Mean Value Theorem for Linear Functionals  
    D. Meek  
    Mathematics of Computation, Vol. 35, No. 151. (Jul., 1980), pp. 797-802, Jstor.  
  67. La réciproque du théorème de moyenne de Cauchy. (French) [The converse of the Cauchy mean-value theorem]
    Stanciu, T. N.
    Bul. Univ. Gala\cedla ti Fasc. II Mat. Fiz. Mec. Teoret. 3 (1980), 47--48, Math. Sci. Net.  
  68. A new mean value theorem and its applications. (Chinese)
    Pan, Cheng Dong
    Chinese Ann. Math. 1 (1980), no. 1, 149--160, Math. Sci. Net.  
  69. Global mean value theorems in thermodynamics.
    Day, W. A.
    Arch. Rational Mech. Anal. 70 (1979), no. 2, 181--188, Math. Sci. Net.  
  70. Application of a Mean Value Theorem for Integrals to Series Summation (in Mathematical Notes)  
    Eberhard L. Stark  
    American Mathematical Monthly, Vol. 85, No. 6. (Jun. - Jul., 1978), pp. 481-483, Jstor.  
  71. A Converse to the Mean Value Theorem for Harmonic Functions  
    William A. Veech  
    American Journal of Mathematics, Vol. 97, No. 4. (Winter, 1975), pp. 1007-1027, Jstor.  
  72. A Zero-One Law for a Class of Random Walks and a Converse to Gauss' Mean Value Theorem  
    William A. Veech  
    The Annals of Mathematics, 2nd Ser., Vol. 97, No. 2. (Mar., 1973), pp. 189-216, pp. 45-46, Jstor.  
  73. A Local Mean Value Theorem for Analytic Function (in Mathematical Notes)  
    Ake Samuelsson  
    American Mathematical Monthly, Vol. 80, No. 1. (Jan., 1973), pp. 45-46, Jstor.  
  74. A Versatile Vector Mean Value Theorem (in Classroom Notes)  
    D. E. Sanderson  
    American Mathematical Monthly, Vol. 79, No. 4. (Apr., 1972), pp. 381-383, Jstor.  
  75. A Note on the Mean Value Theorem (in Mathematical Notes)
    A. A. Goldstein
    American Mathematical Monthly, Vol. 79, No. 1. (Jan., 1972), pp. 51-53, Jstor.  
  76. A Mean Value Theorem (in Mathematical Notes)  
    R. J. Easton, S. G. Wayment  
    American Mathematical Monthly, Vol. 77, No. 2. (Feb., 1970), pp. 170-172, Jstor.  
  77. Integration, Anti-Differentiation and a Converse to the Mean Value Theorem (in Classroom Notes)  
    Howard Levi  
    American Mathematical Monthly, Vol. 74, No. 5. (May, 1967), pp. 585-586, Jstor.  
  78. On Avoiding the Mean Value Theorem (in Classroom Notes)  
    Lipman Bers  
    American Mathematical Monthly, Vol. 74, No. 5. (May, 1967), p. 583, Jstor.  
  79. On Being Mean to the Mean Value Theorem (in Classroom Notes)  
    Leon W. Cohen  
    American Mathematical Monthly, Vol. 74, No. 5. (May, 1967), pp. 581-582, Jstor.  
  80. A Mean Value Theorem-An Extension (in Mathematical Notes)  
    T. V. Lakshminarasimhan  
    American Mathematical Monthly, Vol. 73, No. 8. (Oct., 1966), pp. 862-863, Jstor.  
  81. Mean Value Theorem for Polyharmonic Functions  
    J. H. Bramble, L. E. Payne  
    American Mathematical Monthly, Vol. 73, No. 4, Part 2: Papers in Analysis. (Apr., 1966), pp. 124-127, Jstor.  
  82. A Mean Value Theorem for the Heat Equation  
    W. Fulks  
    Proceedings of the American Mathematical Society, Vol. 17, No. 1. (Feb., 1966), pp. 6-11, Jstor.  
  83. An N-Th Order Second Mean Value Theorem (in Classroom Notes)  
    Donald H. Trahan  
    American Mathematical Monthly, Vol. 72, No. 3. (Mar., 1965), pp. 300-301, Jstor.  
  84. A Mean Value Theorem for an Arbitrary Steady-State Thermoelastic Problem for a Solid Sphere  
    J. L. Nowinski  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 3. (Sep., 1963), pp. 623-631, Jstor.  
  85. A Natural Auxiliary Function for the Mean Value Theorem (in Classroom Notes)  
    M. J. Poliferno  
    American Mathematical Monthly, Vol. 69, No. 1. (Jan., 1962), pp. 45-47, Jstor.  
  86. Sequences Generated by Use of the Mean Value Theorem (in Classroom Notes)  
    Jacqueline P. Evans  
    American Mathematical Monthly, Vol. 68, No. 4. (Apr., 1961), p. 365, Jstor.  
  87. Proof of the Mean Value Theorem (in Classroom Notes)  
    Chung Lie Wang  
    American Mathematical Monthly, Vol. 65, No. 5. (May, 1958), pp. 362-364, Jstor.  
  88. An Application of the Mean Value Theorem (in Classroom Notes)  
    David Zeitlin  
    American Mathematical Monthly, Vol. 64, No. 6. (Jun. - Jul., 1957), p. 427, Jstor.  
  89. On an Application of the Mean Value Theorem (in Classroom Notes)  
    K. A. Bush  
    American Mathematical Monthly, Vol. 62, No. 8. (Oct., 1955), pp. 577-578, Jstor.  
  90. A Proof of the Invariant Mean-Value Theorem on Almost Periodic Functions  
    Hukukane Nikaido  
    Proceedings of the American Mathematical Society, Vol. 6, No. 3. (Jun., 1955), pp. 361-363, Jstor.  
  91. Some Inequalities Arising From a Generalized Mean Value Theorem  
    M. P. Drazin  
    American Mathematical Monthly, Vol. 62, No. 4. (Apr., 1955), pp. 226-232, Jstor.  
  92. Proof of the First Mean Value Theorem of the Integral Calculus (in Classroom Notes)  
    T. Putney  
    American Mathematical Monthly, Vol. 60, No. 2. (Feb., 1953), pp. 113-114, Jstor.  
  93. A Mean Value Theorem in Geometry of Numbers  
    Carl Ludwig Siegel  
    The Annals of Mathematics, 2nd Ser., Vol. 46, No. 2. (Apr., 1945), pp. 340-347, Jstor.  
  94. On the Mean Value Theorem (in Questions, Discussions and Notes)  
    H. L. Krall  
    American Mathematical Monthly, Vol. 42, No. 10. (Dec., 1935), pp. 604-606, Jstor.  
  95. A General Mean-Value Theorem  
    D. V. Widder  
    Transactions of the American Mathematical Society, Vol. 26, No. 3. (Jul., 1924), pp. 385-394, Jstor.  
  96. On the Mean-Value Theorem Corresponding to a Given Linear Homogeneous Differential Equations  
    G. Polya  
    Transactions of the American Mathematical Society, Vol. 24, No. 4. (Dec., 1922), pp. 312-324, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003