한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제18권1호
  • /
  • Pages.63-78
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  • 2011
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  • 1226-0657(pISSN)
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  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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STIELTJES DERIVATIVES AND ITS APPLICATIONS TO INTEGRAL INEQUALITIES OF STIELTJES TYPE

  • 투고 : 2010.10.11
  • 심사 : 2011.02.17
  • 발행 : 2011.02.28
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초록

In the present paper, we obtain integral inequalities involving the Kurzweil-Stieltjes integrals which generalize Gronwall-Bellman inequality and we use the inequalities to verify existence of solutions of a certain integral equation. Such inequalities will play an important role in the study of impulsively perturbed systems [9].

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참고문헌

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  8. B.G. Pachpatte: Inequalities for differential and integral equations. Inequalities for differential and integral equations, Academic Press, Inc., 1998.
  9. S.G. Pandit & S.G. Deo: Differential systems involving impulses. Lecture Notes in Math. 954, Springer-Verlag, Berlin, 1982.
  10. W.F. Pfeffer: The Riemann approach to integration: local geometric theory. Cambridge Tracts in Mathematics 109, Cambridge University Press, 1993.
  11. W. Rudin: Functional analysis. McGraw-Hill, New York, 1973.
  12. H. Schaefer: Uber die methode der a priori-Schranken. Math. Ann. 29 (1955), 415-416.
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피인용 문헌

  1. STIELTJES DERIVATIVE METHOD FOR INTEGRAL INEQUALITIES WITH IMPULSES vol.21, pp.1, 2011, https://doi.org/10.7468/jksmeb.2014.21.1.61