caa a22 4500 605508852 CHVBK 20210128100638.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00010-014-0304-4 doi (NATIONALLICENCE)springer-10.1007/s00010-014-0304-4 Conditionally δ-midconvex functions [Elektronische Daten] [Jacek Chudziak, Jacek Tabor, Józef Tabor] 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. The Author(s), 2014 Midconvex function nationallicence approximately midconvex function nationallicence extremal point nationallicence Chudziak Jacek Faculty of Mathematics and Sciences, University of Rzeszów, ul.Prof. St. Pigonia 1, 35-310, Rzeszów, Poland aut Tabor Jacek Department of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland aut Tabor Józef Faculty of Mathematics and Sciences, University of Rzeszów, ul.Prof. St. Pigonia 1, 35-310, Rzeszów, Poland aut Aequationes mathematicae Springer Basel 89/4(2015-08-01), 981-990 0001-9054 89:4<981 2015 89 10 https://doi.org/10.1007/s00010-014-0304-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-014-0304-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chudziak Jacek Faculty of Mathematics and Sciences, University of Rzeszów, ul.Prof. St. Pigonia 1, 35-310, Rzeszów, Poland aut NATIONALLICENCE 700 1- Tabor Jacek Department of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland aut NATIONALLICENCE 700 1- Tabor Józef Faculty of Mathematics and Sciences, University of Rzeszów, ul.Prof. St. Pigonia 1, 35-310, Rzeszów, Poland aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/4(2015-08-01), 981-990 0001-9054 89:4<981 2015 89 10