Some refinements of Jensen’s inequality. (English) Zbl 0765.26007
Let \(C\) be a convex subset of a real vector space and let \(f\) be a convex function on \(C\). Let \(x_ i\in C\), \(p_ i\geq0\), \(\sum^ n_{i=1}p_ i=1\). The author inserts some expressions between 0 and \(\sum^ n_{i=1}p_ if(x_ i)-f\left(\sum^ n_{i=1}p_ ix_ i\right)\).
Reviewer: I.Raşa (Cluj-Napoca)
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26A51 | Convexity of real functions in one variable, generalizations |
References:
| [1] | Dragomir, S. S.; Ionescu, N. M., A refinement of Jensen inequality (Romanian), (Seminar Didactica Matematicii, Univ. Babeş-Bolyai Cluj, Vol. 5 (1989)), 91-94 |
| [2] | Mitrinović, D. S., Analytic Inequalities (1970), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York · Zbl 0199.38101 |
| [3] | J. E. Pečarić and S. S. Dragomirin; J. E. Pečarić and S. S. Dragomirin |
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