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On Some Bounds for the Parameter λ in Steffensen’s Inequality

Josip Pečarić|Ksenija Smoljak Kalamir
경북대학교 자연과학대학 수학과|2015.12|Kyungpook Mathematical Journal|제55권 제4호|pp. 969-981

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참고문헌

키워드

Steffensen's inequalitygeneralizationsBellman-type inequality
주제분류수학

초록

The object is to obtain weaker conditions for the parameter λ in Steffensen's inequality and its generalizations and refinements additionally assuming nonnegativity of the function f. Furthermore, we contribute to the investigation of the Bellman-type inequalites establishing better bounds for the parameter λ.

Abstract

The object is to obtain weaker conditions for the parameter λ in Steffensen's inequality and its generalizations and refinements additionally assuming nonnegativity of the function f. Furthermore, we contribute to the investigation of the Bellman-type inequalites establishing better bounds for the parameter λ.

참고문헌 (12)

  1. R. Bellman, "On inequalities with alternating signs", Proc. Amer. Math. Soc, 10(5), pp.807~809 (1959)
  2. Z. Liu, "On extensions of Steffensen’s inequality", J. Math. Anal. Approx. Theory, 2(2), pp.132~139 (2007)
  3. P. R. Mercer, "Extensions of Steffensen’s inequality", J. Math. Anal. Appl, 246(1), pp.325~329 (2000)
  4. B. G. Pachpatte, "A note on a certain generalization of Steffensen’s inequality", Octogon Math. Mag, 6(1), pp.46~49 (1998)
  5. J. E. Peˇcari´c, "Notes on some general inequalities", Publ. Inst. Math. (Beograd), (N. S. ), 32(46), pp.131~135 (1982)
  6. J. Peˇcari´c., "Mercer and Wu-Srivastava generalisations of Steffensen’s inequality", Appl. Math. Comput, 219(21), pp.10548~10558 (2013)
  7. J. Peˇcari´c., "Generalized Steffensen type inequalities involving convex functions", J. Funct. Spaces, 2014, pp.10~ (2014)
  8. J. Peˇcari´c., "Steffensen type inequalities involving convex functions", Math. Inequal. Appl, 18(1), pp.363~378 (2015)
  9. J. Peˇcari´c., "New Steffensen type inequalities involving convex functions", Results Math, 67(1), pp.217~234 (2015)
  10. J. Peˇcari´c., "Steffensen’s and related inequalities (A comprehensive survey and recent advances)", Monographs in inequalites, 7 (2014)
  11. J. F. Steffensen, "On certain inequalities between mean values and their application to actuarial problems", Skand. Aktuarietids, 8, pp.2~97 (1918)
  12. S. -H. Wu., "Some improvements and generalizations of Steffensen’s integral inequality", Appl. Math. Comput, 192(2), pp.422~428 (2007)

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