Conditionally δ-midconvex functions
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| 003 | CHVBK | ||
| 005 | 20210128100638.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150801xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-014-0304-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0304-4 | ||
| 245 | 0 | 0 | |a Conditionally δ-midconvex functions |h [Elektronische Daten] |c [Jacek Chudziak, Jacek Tabor, Józef Tabor] |
| 520 | 3 | |a Let X be a real linear space, V be a nonempty subset of X and δ be a nonnegative real number. A function $${f : V \to \mathbb{R}}$$ f : V → R is said to be conditionally δ-midconvex provided $${f(\frac{x+y}{2}) \leq \frac{f(x) + f(y)}{2} + \delta}$$ f ( x + y 2 ) ≤ f ( x ) + f ( y ) 2 + δ for every $${x, y \in V}$$ x , y ∈ V such that $${\frac{x + y}{2} \in V}$$ x + y 2 ∈ V . We show that if V satisfies some reasonable assumptions, then for every bounded from above conditionally δ-midconvex function $${f : V \to \mathbb{R}}$$ f : V → R the following estimation holds: $${\sup f(V) \leq \sup f(ext \, V) + k (V)\delta}$$ sup f ( V ) ≤ sup f ( e x t V ) + k ( V ) δ , where ext V denotes the set of all extremal points of V and k(V) is a respective constant depending on V. | |
| 540 | |a The Author(s), 2014 | ||
| 690 | 7 | |a Midconvex function |2 nationallicence | |
| 690 | 7 | |a approximately midconvex function |2 nationallicence | |
| 690 | 7 | |a extremal point |2 nationallicence | |
| 700 | 1 | |a Chudziak |D Jacek |u Faculty of Mathematics and Sciences, University of Rzeszów, ul.Prof. St. Pigonia 1, 35-310, Rzeszów, Poland |4 aut | |
| 700 | 1 | |a Tabor |D Jacek |u Department of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland |4 aut | |
| 700 | 1 | |a Tabor |D Józef |u Faculty of Mathematics and Sciences, University of Rzeszów, ul.Prof. St. Pigonia 1, 35-310, Rzeszów, Poland |4 aut | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/4(2015-08-01), 981-990 |x 0001-9054 |q 89:4<981 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0304-4 |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/s00010-014-0304-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Chudziak |D Jacek |u Faculty of Mathematics and Sciences, University of Rzeszów, ul.Prof. St. Pigonia 1, 35-310, Rzeszów, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Tabor |D Jacek |u Department of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Tabor |D Józef |u Faculty of Mathematics and Sciences, University of Rzeszów, ul.Prof. St. Pigonia 1, 35-310, Rzeszów, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/4(2015-08-01), 981-990 |x 0001-9054 |q 89:4<981 |1 2015 |2 89 |o 10 | ||