Functional Inequalities Involving Numerical Differentiation Formulas of Order Two

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DC pole	Wartość	Język
dc.contributor.author	Szostok, Tomasz	-
dc.date.accessioned	2018-10-04T10:40:11Z	-
dc.date.available	2018-10-04T10:40:11Z	-
dc.date.issued	2018	-
dc.identifier.citation	Bulletin of the Malaysian Mathematical Sciences Society, Vol. 41, iss. 4 (2018), s. 2053-2066	pl_PL
dc.identifier.issn	0126-6705	-
dc.identifier.uri	http://hdl.handle.net/20.500.12128/6456	-
dc.description.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.	pl_PL
dc.language.iso	en	pl_PL
dc.rights	Uznanie autorstwa 3.0 Polska	*
dc.rights.uri	http://creativecommons.org/licenses/by/3.0/pl/	*
dc.subject	Convex functions	pl_PL
dc.subject	Differentiation formulas	pl_PL
dc.subject	Hermite–Hadamard inequality	pl_PL
dc.title	Functional Inequalities Involving Numerical Differentiation Formulas of Order Two	pl_PL
dc.type	info:eu-repo/semantics/article	pl_PL
dc.identifier.doi	10.1007/s40840-017-0462-3	-
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