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http://hdl.handle.net/20.500.12128/6456| Title: | Functional Inequalities Involving Numerical Differentiation Formulas of Order Two |
| Authors: | Szostok, Tomasz |
| Keywords: | Convex functions; Differentiation formulas; Hermite–Hadamard inequality |
| Issue Date: | 2018 |
| Citation: | Bulletin of the Malaysian Mathematical Sciences Society, Vol. 41, iss. 4 (2018), s. 2053-2066 |
| Abstract: | We write expressions connected with numerical differentiation formulas of order 2 in the form of Stieltjes integral, then we use Ohlin lemma and Levin–Stechkin theorem to study inequalities connected with these expressions. In particular, we present a new proof of the inequality f(x+y2)≤1(y-x)2∫xy∫xyf(s+t2)dsdt≤1y-x∫xyf(t)dtsatisfied by every convex function f:R→R and we obtain extensions of this inequality. Then we deal with non-symmetric inequalities of a similar form. |
| URI: | http://hdl.handle.net/20.500.12128/6456 |
| DOI: | 10.1007/s40840-017-0462-3 |
| ISSN: | 0126-6705 |
| Appears in Collections: | Artykuły (WNŚiT) |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| Szostok_Functional_inequalities_involving_numerical_differentiation_formulas.pdf | 520,63 kB | Adobe PDF | View/Open |
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