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

Kim, Young-Ho

Proc. Japan Acad., Ser. A 77, No. 10, 164-167 (2001).

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.

Reviewer: Ion Raşa (Cluj-Napoca)

MSC:

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

Keywords:

integral inequalities; convex functions

Citations:

Zbl 0738.26006

References:

[1]	Borell, C.: Integral inequalities for generalised concave and convex functions. J. Math. Anal. Appl., 43 , 419-440 (1973). · Zbl 0265.26012
[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
[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