On Gronwall and Wendroff type inequalities
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- by J. Abramowich PDF
- Proc. Amer. Math. Soc. 87 (1983), 481-486 Request permission
Abstract:
It is shown how Gronwall’s Lemma and the extension to many variables given by W. Walter may be derived using the simple method of recursion. This same method is used to extend this result and to derive a more general Wendroff type inequality. Upper and lower bounds for the Neumann series in the case of two independent variables are given.References
- Wolfgang Walter, Differential and integral inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 55, Springer-Verlag, New York-Berlin, 1970. Translated from the German by Lisa Rosenblatt and Lawrence Shampine. MR 0271508
- B. K. Bondge, B. G. Pachpatte, and Wolfgang Walter, On generalized Wendroff-type inequalities and their applications, Nonlinear Anal. 4 (1980), no. 3, 491–495. MR 574367, DOI 10.1016/0362-546X(80)90086-3
- Donald R. Snow, A two independent variable Gronwall-type inequality, Inequalities, III (Proc. Third Sympos., Univ. California, Los Angeles, Calif., 1969; dedicated to the memory of Theodore S. Motzkin), Academic Press, New York, 1972, pp. 333–340. MR 0338537
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 481-486
- MSC: Primary 34A40; Secondary 26D15
- DOI: https://doi.org/10.1090/S0002-9939-1983-0684643-6
- MathSciNet review: 684643