# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
On some integral inequalities similar to Bellman-Bihari inequalities. (English) Zbl 0305.26009

##### MSC:
 26D10 Inequalities involving derivatives, differential and integral operators 45D05 Volterra integral equations
Full Text:
##### 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