Functional inequalities involving numerical differentiation formulas of\n order two

2016/08/31 by Tomasz Szostok, Szostok, Tomasz
Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #Composite Structure Analysis and Optimization #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.1608.08937

openalex publication_date 2016/08/31 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/28

Abstract

We write expressions connected with numerical differentiation formulas of\norder 2 in the form of Stieltjes integral, then we use Ohlin lemma and\nLevin-Stechkin theorem to study inequalities connected with these expressions.\nIn particular, we present a new proof of the inequality n
labelDr\n f
left(
fracx+y2
right)
leq
frac1(y-x)²
int_x^y
hspace-2mm
int_x^yf
left(
fracs+t2
right)ds
:dt\n
leq
frac1y-x
int_x^yf(t)dt satisfied by every convex\nfunction f: R\→ R and we obtain extensions of\n rfDr.\n Then we deal with\n nonsymmetric inequalities of a similar form.\n

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