×

Hadamard-type inequalities for s-convex functions. (English) Zbl 1193.26020

Summary: We establish some new inequalities for differentiable functions based on concavity and \(s\)-convexity. We also prove several Hadamard-type inequalities for products of two convex and \(s\)-convex functions.

MSC:

26D15 Inequalities for sums, series and integrals
26A51 Convexity of real functions in one variable, generalizations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Hudzik, H.; Maligranda, L., Some remarks on \(s\)-convex functions, Aequationes Math., 48, 100-111 (1994) · Zbl 0823.26004
[2] Pečarić, J. E.; Proschan, F.; Tong, Y. L., Convex Functions, Partial Orderings, and Statistical Applications (1992), Academic Press Inc., p. 137 · Zbl 0749.26004
[3] Kirmaci, U. S., Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput., 147, 91-95 (2004) · Zbl 1043.26012
[4] Özdemir, M. E.; Kırmaci, U. S., Two new theorems on mappings uniformly continuous and convex with applications to quadrature rules and means, Appl. Math. Comput., 143, 269-274 (2003) · Zbl 1020.26012
[5] Pachpatte, B. G., Inequalities for Differentiable and Integral Equations (1997), Academic Press Inc. · Zbl 0879.34013
[6] Dragomir, S. S.; Fitzpatrick, S., The Hadamard’s inequality for \(s\)-convex functions in the second sense, Demonstratio Math., 32, 4, 687-696 (1999) · Zbl 0952.26014
[7] B. Jagers, On a Hadamard-type inequality for \(s\)-convex functions. http://wwwhome.cs.utwente.nl/ jagersaa/alphaframes/Alpha.pdf.; B. Jagers, On a Hadamard-type inequality for \(s\)-convex functions. http://wwwhome.cs.utwente.nl/ jagersaa/alphaframes/Alpha.pdf.
[8] Dragomir, S. S.; Agarwal, R. P., Two inequalities for differentiable mappings and applications to special means of real numbers and trapezoidal formula, Appl. Math. Lett., 5, 91-95 (1998) · Zbl 0938.26012
[9] Özdemir, M. E., A theorem on mappings with bounded derivatives with applications to quadrature rules and means, Appl. Math. Comput., 138, 425-434 (2003) · Zbl 1033.26023
[10] Pearce, C. E.M.; Pečarić, J., Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett., 13, 51-55 (2000) · Zbl 0970.26016
[11] Pachpatte, B. G., On some inequalities for convex functions, RGMIA Res. Rep. Coll., 6, E (2003) · Zbl 1050.26019
[12] Mitrinović, D. S.; Pečarić, J. E.; Fink, A. M., Classical and New Inequalities in Analysis (1993), Kluwer Academic Publishers, p. 106, 10, 15 · Zbl 0771.26009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.