The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지

ESTIMATION OF DIFFERENCE FROM H$\ddot{O}$LDER'S INEQUALITY

  • Received : 2010.03.15
  • Accepted : 2010.05.10
  • Published : 2010.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

We give an upper bound for the estimation of the difference between both sides of the well-known H$\ddot{o}$lder's inequality. Moreover, an upper bound for the estimation of the difference of the integral form of H$\ddot{o}$lder's inequality is also obtained. The results of this paper are natural generalizations and refinements of those of [2-4].

Keywords

References

  1. E.F. Beckenbach & R. Bellman: Inequalities. Springer Verlag, Berlin, 1961.
  2. S. Izumino: Ozeki's method on Holder's inequality. Math. Japon. 50 (1999), 41-551.
  3. S. Izumino, H. Mori & Y. Seo: On Ozeki's inequality. Math.Inequal. Appl. 4 (2001), 163-187.
  4. S. Izumino, J. Pecaric & M. Tominaga: Difference derived from weighted Holder's inequality. Math.Inequal. Appl. 8 (2005), 337-345.
  5. D.S. Mitrinovic, J.E. Pecaric & A.M. Fink: Classical and new inequalities in analysis. Kluwer Acad. Publ., Dordrecht, 1993.
  6. N. Ozeki: On the estimation of the inequalities by the maximum, or minimum values(in Japanese). J. College Arts Sci. Chiba Univ. 5 (1968), 199-203.