Ashyralyev, Allaberen; Misirli, Emine; Mogol, Ozlem A note on the integral inequalities with two dependent limits. (English) Zbl 1197.26023 J. Inequal. Appl. 2010, Article ID 430512, 18 p. (2010). Summary: The theorem on the Gronwall’s type integral inequalities with two dependent limits is established. As application, the boundedness of the solutions of nonlinear differential equations is presented. Cited in 4 Documents MSC: 26D15 Inequalities for sums, series and integrals PDFBibTeX XMLCite \textit{A. Ashyralyev} et al., J. Inequal. Appl. 2010, Article ID 430512, 18 p. (2010; Zbl 1197.26023) Full Text: DOI EuDML References: [1] Agarwal RP: Difference Equations and Inequalities: Theory, Methods and Applications, Monographs and Textbooks in Pure and Applied Mathematics. Volume 155. Marcel Dekker, New York, NY, USA; 1992:xiv+777. [2] Beckenbach EF, Bellman R: Inequalities. Springer, New York, NY, USA; 1965:xi+198. · Zbl 0128.27401 [3] Mitrinović DS: Analytic Inequalities. Springer, New York, NY, USA; 1970:xii+400. · Zbl 0199.38101 [4] Gronwall TH: Note on the derivatives with respect to a parameter of the solutions of a system of differential equations. Annals of Mathematics II 1919, 20(4):292-296. · JFM 47.0399.02 [5] Pachpatte BG: Some new finite difference inequalities. Computers & Mathematics with Applications 1994, 28(1-3):227-241. · Zbl 0809.26009 [6] Kurpınar E: On inequalities in the theory of differential equations and their discrete analogues. Pan-American Mathematical Journal 1999, 9(4):55-67. · Zbl 0961.26008 [7] Pachpatte BG: On the discrete generalizations of Gronwall’s inequality. Journal of Indian Mathematical Society 1973, 37: 147-156. · Zbl 0331.26017 [8] Pachpatte BG: Inequalities for Differential and Integral Equations, Mathematics in Science and Engineering. Volume 197. Academic Press, New York, NY, USA; 1998:x+611. · Zbl 1032.26008 [9] Mamedov YDj, Ashirov S: A Volterra type integral equation. Ukrainian Mathematical Journal 1988, 40(4):510-515. · Zbl 0653.45005 [10] Ashyraliyev M: Generalizations of Gronwall’s integral inequality and their discrete analogies. Report September 2005., (MAS-EO520): [11] Ashyraliyev, M., Integral inequalities with four variable limits, 170-184 (1998) [12] Ashyraliyev M: A note on the stability of the integral-differential equation of the hyperbolic type in a Hilbert space. Numerical Functional Analysis and Optimization 2008, 29(7-8):750-769. 10.1080/01630560802292069 · Zbl 1146.45001 [13] Ashirov S, Kurbanmamedov N: Investigation of the solution of a class of integral equations of Volterra type. Izvestiya Vysshikh Uchebnykh Zavedeniĭ. Matematika 1987, 9: 3-9. · Zbl 0635.45015 [14] Corduneanu A: A note on the Gronwall inequality in two independent variables. Journal of Integral Equations 1982, 4(3):271-276. · Zbl 0526.26008 [15] Fattorini HO: Second Order Linear Differential Equations in Banach Spaces, Notas de Matematica, North-Holland Mathematics Studies. Volume 108. North-Holland, Amsterdam, The Netherlands; 1985:xiii+314. [16] Piskarev S, Shaw S-Y: On certain operator families related to cosine operator functions. Taiwanese Journal of Mathematics 1997, 1(4):3585-3592. · Zbl 0906.47030 [17] Ashyralyev A, Aggez N: A note on the difference schemes of the nonlocal boundary value problems for hyperbolic equations. Numerical Functional Analysis and Optimization 2004, 25(5-6):439-462. 10.1081/NFA-200041711 · Zbl 1065.35021 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.