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 | References | Similar Articles | Additional Information

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**].

**[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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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