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On some integral inequalities similar to Bellman-Bihari inequalities. (English) Zbl 0305.26009

MSC:
26D10Inequalities involving derivatives, differential and integral operators
45D05Volterra integral equations
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Full Text: DOI
References:
[1] Bellman, R.; Cooke, K. L.: Differential-difference equations. (1963) · Zbl 0105.06402
[2] Bihari, I.: A generalization of lemma of Bellman and its applications to uniqueness problems of differential equations. Acta math. Acad. sci. Hung. 7, 81-94 (1956) · Zbl 0070.08201
[3] Deo, S. G.; Murdeshwar, M. G.: A note on Gronwall’s inequality. Bull. London math. Soc. 3, 34-36 (1972) · Zbl 0223.26011
[4] Dhongade, U. D.; Deo, S. G.: Some generalizations of Bellman-bihari integral inequalities. J. math. Anal. appl. 44, 218-226 (1973) · Zbl 0275.45018
[5] Gronwall, T. H.: Note on the derivatives with respect to a parameter of the solutions of a system of differential equations. Ann. math. 20, 292-296 (1919) · Zbl 47.0399.02
[6] Pachpatte, B. G.: A note on Gronwall-Bellman inequality. J. math. Anal. appl. 44, 758-762 (1973) · Zbl 0274.45011
[7] Pachpatte, B. G.: A note on integral inequalities of the Bellman-bihari type. J. math. Anal. appl. 49, 295-301 (1975)
[8] Pachpatte, B. G.: An integral inequality similar to Bellman-bihari inequality. Bull. soc. Math. grêce 15, 7-12 (1974) · Zbl 0308.26007
[9] Pachpatte, B. G.: Integral inequalities of the Gronwall-Bellman type and their applications. J. math. Phys. sci. 8, 309-318 (1974) · Zbl 0292.45017
[10] Pachpatte, B. G.: Integral perturbations of nonlinear systems of differential equations. Bull. soc. Math. grêce 14, 92-97 (1973) · Zbl 0295.34040