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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.
DOI: 10.1007/s40840-017-0462-3
ISSN: 0126-6705
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