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http://dx.doi.org/10.7468/jksmeb.2016.23.2.181

SOME RETARDED INTEGRAL INEQUALITIES AND THEIR APPLICATIONS  

KIM, YOUNG JIN (DANG JIN MIDDLE SCHOOL)
Publication Information
The Pure and Applied Mathematics / v.23, no.2, 2016 , pp. 181-199 More about this Journal
Abstract
In this paper we obtain some retarded integral inequalities involving Stieltjes derivatives and we use our results in the study of various qualitative properties of a certain retarded impulsive differential equation.
Keywords
retarded integral inequalities; Stieltjes derivatives; retarded impulsive differential equations;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 D. Frănková: Regulated functions. Math. Bohem. 116(1991), 20-59.
2 C.S. Hönig: Volterra Stieltjes-integral equations. Mathematics Studies 16, North-Holand and American Elsevier, Amsterdam and New York, 1973.
3 Y.J. Kim: Stieltjes derivatives and its applications to integral inequalities of Stieltjes type. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 18 (2011), no. 1, 63-78.
4 ______: Stieltjes derivative method for integral inequalities with impulses. J. Korean Soc. Math. Educ.Ser. B: Pure Appl. Math. 21 (2014), no. 1, 61-75.
5 B. G. Pachpatte: Inequalities for differential and integral equations. Mathematics in Science and Engineering 197, Academic Press, Inc., 1998.
6 ______: Integral and finite difference inequalities and applications. Mathematics Studies 205, North-Holand and American Elsevier, Amsterdam and New York, 2006.
7 W. Rudin: Functional analysis. McGraw-Hill, New York, 1973.
8 Š. Schwabik: Generalized ordinary differential equations. World Scientific, Singapore, 1992.
9 A.M. Samoilenko & N.A. Perestyuk: Impulsive differential equations. World Scientific, Singapore, 1995.
10 H. Schaefer: Über die methode der a priori-Schranken. Math. Ann. 29 (1955), 415-416.
11 Š. Schwabik, M. Tvrdý & O. Vejvoda: Differntial and integral equations: boundary value problems and adjoints. Academia and D. Reidel, Praha and Dordrecht, 1979.
12 M. Tvrdý: Regulated functions and the Perron-Stieltjes integral. Časopis pešt. mat. 114 (1989), no. 2, 187-209.