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Kirmaci, U. S.; Klaričić Bakula, M.; Özdemir, M. E.; Pečarić, J.

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

Appl. Math. Comput. 193, No. 1, 26-35 (2007).
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.

Cited in 87 Documents

MSC:

26D15 Inequalities for sums, series and integrals
26A51 Convexity of real functions in one variable, generalizations

Keywords:

Hadamard’s inequality; \(s\)-convex functions; convex functions; product of two functions
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\textit{U. S. Kirmaci} et al., Appl. Math. Comput. 193, No. 1, 26--35 (2007; Zbl 1193.26020)
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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
[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
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