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Generalized retarded integral inequalities. (English) Zbl 1171.26328
Summary: We prove some new retarded integral inequalities. The results generalize those in [Y. G. Sun, J. Math. Anal. Appl. 301, No. 2, 265–275 (2005; Zbl 1057.26022)].

##### MSC:
 26D15 Inequalities for sums, series and integrals of real functions
##### References:
 [1] Agarwal, R. P.; Ryoo, C. S.; Kim, Y. -Ho: New integral inequalities for iterated integrals with applications, J. inequal. Appl. (2007) · Zbl 1133.26304 · doi:10.1155/2007/24385 [2] R.A.C. Ferreira, D.F.M. Torres, Generalizations of Gronwall-Bihari inequalities on time scales, J. Difference Equ. Appl., in press (doi:10.1080/10236190802213276) [3] Jiang, F.; Meng, F.: Explicit bounds on some new nonlinear integral inequalities with delay, J. comput. Appl. math. 205, No. 1, 479-486 (2007) · Zbl 1135.26015 · doi:10.1016/j.cam.2006.05.038 [4] Lipovan, O.: A retarded integral inequality and its applications, J. math. Anal. appl. 285, No. 2, 436-443 (2003) · Zbl 1040.26007 · doi:10.1016/S0022-247X(03)00409-8 [5] Lipovan, O.: Integral inequalities for retarded Volterra equations, J. math. Anal. appl. 322, No. 1, 349-358 (2006) · Zbl 1103.26018 · doi:10.1016/j.jmaa.2005.08.097 [6] Ma, Q. -H.; Pečarić, J.: Some new nonlinear retarded integral inequalities and their applications, Math. inequal. Appl. 9, No. 4, 617-632 (2006) · Zbl 1122.26023 [7] Ma, Q. -H.; Pečarić, J.: Some new retarded Volterra–Fredholm type integral inequalities with power nonlinear and their applications, Math. inequal. Appl. 10, No. 4, 811-826 (2007) · Zbl 1129.26014 [8] Ma, Q. -H.; Pečarić, J.: On some new nonlinear retarded integral inequalities with iterated integrals and their applications, J. korean math. Soc. 45, No. 2, 331-353 (2008) · Zbl 1153.26314 · doi:10.4134/JKMS.2008.45.2.331 [9] Ou-Yang-Liang: The boundedness of solutions of linear differential equations y”+$A\left(t\right)$y=0, Adv. math. 3, 409-415 (1957) [10] Pachpatte, B. G.: On some new inequalities related to certain inequalities in the theory of differential equations, J. math. Anal. appl. 189, No. 1, 128-144 (1995) · Zbl 0824.26010 · doi:10.1006/jmaa.1995.1008 [11] Sun, Y. G.: On retarded integral inequalities and their applications, J. math. Anal. appl. 301, No. 2, 265-275 (2005) · Zbl 1057.26022 · doi:10.1016/j.jmaa.2004.07.020 [12] Xu, R.; Sun, Y. G.: On retarded integral inequalities in two independent variables and their applications, Appl. math. Comput. 182, No. 2, 1260-1266 (2006) · Zbl 1118.26025 · doi:10.1016/j.amc.2006.05.013 [13] Zhao, P.; Meng, F.; Zhao, Y.: A generalization of a retarded inequality and its applications, Ann. differential equations 22, No. 1, 113-118 (2006) · Zbl 1094.26024