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Wendroff type inequalities


Authors: R. P. Shastri and D. Y. Kasture
Journal: Proc. Amer. Math. Soc. 72 (1978), 248-250
MSC: Primary 35B45; Secondary 34A40, 45K05
DOI: https://doi.org/10.1090/S0002-9939-1978-0507316-7
Erratum: Proc. Amer. Math. Soc. 75 (1979), 374.
MathSciNet review: 507316
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Abstract: Results (1) and (3) of Wendroff on two-variable scalar integral inequalities, quoted without proof by Beckenback and Bellman [1, p. 154] have been generalized to cover a system of integral inequalities by following an approach different from that of Jagdish Chandra and Davis [3].


References [Enhancements On Off] (What's this?)

  • [1] E. F. Beckenback and R. Bellman, Inequalities, Ergebnisse der Math., Springer-Verlag, Berlin and New York, 1961, p. 154. MR 0158038 (28:1266)
  • [2] S. Ghoshal and M. Abu. Masood, Gronwall's vector inequality and its application to a class of non-self adjoint linear and non-linear hyperbolic partial differential equations, J. Indian Math. Soc. 38 (1974), 383-394. MR 0445129 (56:3474)
  • [3] Jagdish Chandra and Paul W. Davis, Linear generalizations of Gronwall's inequality, Proc. Amer. Math. Soc. 60 (1976), 157-160. MR 0422735 (54:10721)
  • [4] V. Lakshmikantham and S. Leela, Differential and integral inequalities, Vol. II, Academic Press, New York, 1969, p. 224.
  • [5] D. R. Snow, Gronwall's inequality for systems of partial differential equations in two independent variables, Proc. Amer. Math. Soc. 33 (1972), 46-54. MR 0298188 (45:7240)
  • [6] W. G. Walter, Differential and integral inequalities, Springer-Verlag, Berlin and New York, 1970. MR 0271508 (42:6391)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0507316-7
Keywords: Wendroff's inequality, integral inequality, differential inequality, integral equation
Article copyright: © Copyright 1978 American Mathematical Society

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