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On some Pachpatte integral inequalities involving convex functions. (English) Zbl 1025.26014

B. G. Pachpatte [“On some integral inequalities involving convex functions”, RGMIA Res. Rep. Coll. 3(3), Article 16( 2000)] established some integral inequalities involving convex functions defined on real intervals. By using the results of J. E. Pečarić and S. S. Dragomir [“A generalization of Hadamard’s inequality for isotonic linear functionals ”, Rad. Mat. 7, 103-107 (1991; Zbl 0738.26006)] as well as an elementary analysis the author generalizes Pachpatte’s inequalities.

MSC:

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

Citations:

Zbl 0738.26006
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References:

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[2] Dragomir, S. S., and Ionescu, N. M.: Some remarks on convex functions. Anal. Num. Theor. Approx., 21 , 31-36 (1992). · Zbl 0770.26008
[3] Heinig, H. P., and Maligranda, L.: Chebyshev inequality in functions spaces. Real Anal. Exchange, 17 , 211-247 (1991/92)
[4] Maligranda, L., Pečarić, J. E., and Persson, L. E.: On some inequalities of the Gröss-Barnes and Borell type. J. Math. Anal. Appl., 187 , 306-323 (1994). · Zbl 0851.26013 · doi:10.1006/jmaa.1994.1358
[5] Mitrinović, D. S.: Analytic Inequalities. Springer, Berin-New York (1970). · Zbl 0199.38101
[6] Pachpatte, B. G.: On some integral inequalities involving convex functions. RGMIA Research Report Collection, 3 (3), Article 16 (2000). · Zbl 0991.26009
[7] Pečarić, J. E., and Dragomir, S. S.: A generalization of Hadamard’s inequality for isotonic linear functionals. Radovi Matematicki, 7 , 103-107 (1991). · Zbl 0738.26006
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