On Ostrowski-type inequalities for functions whose derivatives are m-convex and (alph, m)-convex functions with applications
Abstract
Keywords
Full Text:
PDFReferences
M. Alomari, M. Darus, S.S. Dragomir and P. Cerone, Ostrowski's inequalities for functions whose derivatives are $s$-convex in the second sense, Appl. Math. Lett., Volume 23 (9) (2010), 1071--1076.
M. Alomari, M. Darus, Some Ostrowski type inequalities for convex functions with applications, RGMIA13 (1) (2010) article No. 3. Preprint.
M. Alomari, M. Darus, Some Ostrowski type inequalities for quasi-convex functions with applications to special means, RGMIA13 (2) (2010) article No. 3. Preprint.
A. M. Bruckner and E. Ostrow, Some function classes related to the class of convex functions, Pacific J. Math., 12(1962), 1203--1215.
M. K. Bakula, M. E. Ozdemir and J. Pevcaric, Hadamard type inequalities for $m$-convex and $left( alpha,mright) $-convex functions, J. Inequal. Pure & Appl. Math.,9(2008), Article 96.[ONLINE:htpp://jipam.vu.edu.au]
M. K Bakula, J. Pevcaric, and M. Ribivcic, Companion inequalities to Jensen's inequality for $m$-convex and $left(alpha ,mright) $-convex functions convex functions, J. Inequal. Pure & Appl. Math., 7(2006), Article 194. [ONLINE:htpp://jipam.vu.edu.au]
P. Cerone and S.S. Dragomir, Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions, Demonstratio Math., 37 (2004), no. 2, 299—308
S. S. Dragomir and G. Toader, Some inequalities for $m$-convex functions, Studia Univ. Babecs-Bolyai Math.,38(1) (1993), 21--28.
S. S. Dragomir , Two mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl., 167 (1992), 49--56.
S.S. Dragomir and Th. M. Rassias, (Eds) Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publishers, Dordrecht/Boston/London, 2002.
[ 11] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.Online:[http://www.staff.vu.edu.au/RGMIA/monographs/hermite/_hadamard.html].
Havva Kavurmaci, M. Emin Ozdemir and Merve Avci, New Ostrowski type inequalityes for $m$-convex functions and applications, Hacettepe Journal of Mathematics and Statistics, Volume 40 (2) (2011), 135-145.
V.G. Mihecsan, A generalization of the convexity, Seminar on Functional Equations, Approx. and Convex., Cluj-Napoca (Romania) (1993).
M. E. Ozdemir M. Avci and H. Kavurmaci, Hermite-Hadamard-type inequalities via $left( alpha,mright) $-convexity, Computers & Mathematics with Applications, Volume 61(9) (2011), 2614--2620.
M. E Odemir, H. Kavurmac and E. Set, Ostrowski's type inequalities for $left( alpha,mright) $-onvex functions, Kyungpook Math. J.,50(2010), 371--378.
J.E. Pevcaric, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Academic Press Inc., 1992, p.137
G. H. Toader, Some generalizations of the convexity, Proc. Colloq. Approx. Optim, Cluj-Napoca(Romania), 1984, 329--338.
G. Toader, On a generalization of the convexity, Mathematica, 30 (53) (1988), 83--87.
S. Toader, The order of a star-convex function, Bull. Applied & Comp. Math.,85-B(1998), BAM-1473, 347--350.
DOI: http://dx.doi.org/10.5556/j.tkjm.43.2012.653
Sponsored by Tamkang University | ISSN 0049-2930 (Print), ISSN 2073-9826 (Online) |