Ohlin's lemma and some inequalities of the Hermite-Hadamard type
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| 008 | 210128e20150601xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-014-0286-2 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0286-2 | ||
| 100 | 1 | |a Szostok |D Tomasz |u Institute of Mathematics, University of Silesia, Bankowa 14, 40-007, Katowice, Poland |4 aut | |
| 245 | 1 | 0 | |a Ohlin's lemma and some inequalities of the Hermite-Hadamard type |h [Elektronische Daten] |c [Tomasz Szostok] |
| 520 | 3 | |a Using the Ohlin lemma on convex stochastic ordering we prove inequalities of the Hermite-Hadamard type. Namely, we determine all numbers $${a,\alpha,\beta\in[0,1]}$$ a , α , β ∈ [ 0 , 1 ] such that for all convex functions f the inequality $$af(\alpha x+(1-\alpha )y)+(1-a)f(\beta x+(1-\beta) y)\leq \frac{1}{y-x} \int\limits_{x}^yf(t)dt$$ a f ( α x + ( 1 - α ) y ) + ( 1 - a ) f ( β x + ( 1 - β ) y ) ≤ 1 y - x ∫ x y f ( t ) d t is satisfied and all $${a,b,c,\alpha\in(0,1)}$$ a , b , c , α ∈ ( 0 , 1 ) with a+b+c=1 for which we have $$af(x)+bf(\alpha x+(1-\alpha)y)+cf(y)\geq\frac{1}{y-x} \int\limits_{x}^yf(t)dt$$ a f ( x ) + b f ( α x + ( 1 - α ) y ) + c f ( y ) ≥ 1 y - x ∫ x y f ( t ) d t . | |
| 540 | |a The Author(s), 2014 | ||
| 690 | 7 | |a Convex functions |2 nationallicence | |
| 690 | 7 | |a Hermite-Hadamard inequalities |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 915-926 |x 0001-9054 |q 89:3<915 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0286-2 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-014-0286-2 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Szostok |D Tomasz |u Institute of Mathematics, University of Silesia, Bankowa 14, 40-007, Katowice, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 915-926 |x 0001-9054 |q 89:3<915 |1 2015 |2 89 |o 10 | ||