On Gronwall and Wendroff type inequalities
Author: J. Abramowich
Journal: Proc. Amer. Math. Soc. 87 (1983), 481-486
MSC: Primary 34A40; Secondary 26D15
MathSciNet review: 684643
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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.
-  Wolfgang Walter, Differential and integral inequalities, Translated from the German by Lisa Rosenblatt and Lawrence Shampine. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 55, Springer-Verlag, New York-Berlin, 1970. 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, https://doi.org/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
- W. Walter, Differential and integral inequalities, Springer-Verlag, New York, 1970. MR 0271508 (42:6391)
- B. K. Bondge, B. G. Pachpatte and W. Walter, On generalized Wendroff type inequalities and their applications, Nonlinear Analysis, Theory, Methods & Applications 4 (1980). MR 574367 (81g:26007)
- D. R. Snow, A two independent variable Gronwall type inequality, Inequalities III, Academic Press, New York, 1971, pp. 330-340. MR 0338537 (49:3301)
Keywords: Integral inequality, Gronwall, Wendroff, recursion
Article copyright: © Copyright 1983 American Mathematical Society