Browse > Article
http://dx.doi.org/10.5666/KMJ.2015.55.4.969

On some Bounds for the Parameter λ in Steffensen's Inequality  

PECARIC, JOSIP (Faculty of Textile Technology, University of Zagreb)
KALAMIR, KSENIJA SMOLJAK (Faculty of Textile Technology, University of Zagreb)
Publication Information
Kyungpook Mathematical Journal / v.55, no.4, 2015 , pp. 969-981 More about this Journal
Abstract
The object is to obtain weaker conditions for the parameter ${\lambda}$ 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 ${\lambda}$.
Keywords
Steffensen's inequality; generalizations; Bellman-type inequality;
Citations & Related Records
연도 인용수 순위
  • Reference
1 R. Bellman, On inequalities with alternating signs, Proc. Amer. Math. Soc., 10(5)(1959), 807-809.   DOI
2 Z. Liu, On extensions of Steffensen's inequality, J. Math. Anal. Approx. Theory, 2(2)(2007), 132-139.
3 P. R. Mercer, Extensions of Steffensen's inequality, J. Math. Anal. Appl., 246(1)(2000), 325-329.   DOI
4 B. G. Pachpatte, A note on a certain generalization of Steffensen's inequality, Octogon Math. Mag., 6(1)(1998), 46-49.
5 J. E. Pecaric, Notes on some general inequalities, Publ. Inst. Math. (Beograd), (N. S.), 32(46)(1982), 131-135.
6 J. Pecaric, A. Perusic and K. Smoljak, Mercer and Wu-Srivastava generalisations of Steffensen's inequality, Appl. Math. Comput., 219(21)(2013), 10548-10558.   DOI
7 J. Pecaric and K. Smoljak Kalamir, Generalized Steffensen type inequalities involving convex functions, J. Funct. Spaces, 2014(2014), Article ID 428030, 10 pages.
8 J. Pecaric and K. Smoljak, Steffensen type inequalities involving convex functions, Math. Inequal. Appl., 18(1)(2015), 363-378.
9 J. Pecaric and K. Smoljak Kalamir, New Steffensen type inequalities involving convex functions, Results Math., 67(1)(2015), 217-234.   DOI
10 J. Pecaric, K. Smoljak Kalamir and S. Varosanec, Steffensen's and related inequalities (A comprehensive survey and recent advances), Monographs in inequalites 7, Element, Zagreb, 2014.
11 J. F. Steffensen, On certain inequalities between mean values and their application to actuarial problems, Skand. Aktuarietids., (1918), 82-97.
12 S.-H. Wu and H. M. Srivastava, Some improvements and generalizations of Steffensen's integral inequality, Appl. Math. Comput., 192(2)(2007), 422-428.   DOI