Convexity with respect to families of means
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| 001 | 60550816X | ||
| 003 | CHVBK | ||
| 005 | 20210128100635.0 | ||
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| 008 | 210128e20150201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-014-0281-7 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0281-7 | ||
| 245 | 0 | 0 | |a Convexity with respect to families of means |h [Elektronische Daten] |c [Gyula Maksa, Zsolt Páles] |
| 520 | 3 | |a In this paper we investigate continuity properties of functions $${f : \mathbb {R}_+ \to \mathbb {R}_+}$$ f : R + → R + that satisfy the (p, q)-Jensen convexity inequality $$f\big(H_p(x, y)\big) \leq H_q(f(x), f(y)) \qquad(x, y > 0),$$ f ( H p ( x , y ) ) ≤ H q ( f ( x ) , f ( y ) ) ( x , y > 0 ) , where H p stands for the pth power (or Hölder) mean. One of the main results shows that there exist discontinuous multiplicative functions that are (p, p)-Jensen convex for all positive rational numbers p. A counterpart of this result states that if f is (p, p)-Jensen convex for all $${p \in P \subseteq \mathbb {R}_+}$$ p ∈ P ⊆ R + , where P is a set of positive Lebesgue measure, then f must be continuous. | |
| 540 | |a Springer Basel, 2014 | ||
| 690 | 7 | |a Convexity |2 nationallicence | |
| 690 | 7 | |a Jensen convexity |2 nationallicence | |
| 690 | 7 | |a Hölder means |2 nationallicence | |
| 690 | 7 | |a derivation |2 nationallicence | |
| 700 | 1 | |a Maksa |D Gyula |u Institute of Mathematics, University of Debrecen, Pf.12, 4010, Debrecen, Hungary |4 aut | |
| 700 | 1 | |a Páles |D Zsolt |u Institute of Mathematics, University of Debrecen, Pf.12, 4010, Debrecen, Hungary |4 aut | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/1(2015-02-01), 161-167 |x 0001-9054 |q 89:1<161 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0281-7 |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/s00010-014-0281-7 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Maksa |D Gyula |u Institute of Mathematics, University of Debrecen, Pf.12, 4010, Debrecen, Hungary |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Páles |D Zsolt |u Institute of Mathematics, University of Debrecen, Pf.12, 4010, Debrecen, Hungary |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/1(2015-02-01), 161-167 |x 0001-9054 |q 89:1<161 |1 2015 |2 89 |o 10 | ||