Conditionally approximately convex functions

• Autorzy: Najdecki A. , Tabor J.
• Języki publikacji: EN

Abstrakty

EN

Let X be a real normed space, V be a subset of X and α: [0, ∞) → [0, ∞) be a nondecreasing function. We say that a function f : V → [-∞, ∞) is conditionally α-convex if for each convex combination (…) of elements from V such that (…), the following inequality holds true (…). We present some necessary and some sufficient conditions for f to be conditionally α-convex.

Słowa kluczowe

EN

convex function; approximately convex function; conditionally convex function

PL

funkcja wypukła

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2016
• Tom: Vol. 49, nr 1
• Strony: 11--17
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Najdecki A.

• Faculty of Mathematics and Natural Sciences University of Rzeszów Rejtana 16a 35-959 Rzeszów, Poland

autor

Tabor J.

• Faculty of Mathematics and Natural Sciences University of Rzeszów Rejtana 16a 35-959 Rzeszów, Poland

Bibliografia

• [1] A. Daniilidis, P. Georgiev, Approximate convexity and submonotonicity, J. Math. Anal. Appl. 291 (2004), 292–301.
• [2] A. Házy, On approximate t-convexity, Math. Inequal. Appl. 8(3) (2005), 389–402.
• [3] D. H. Hyers, S. M. Ulam, Approximately convex functions, Proc. Amer. Math. Soc. 3 (1952), 821–828.
• [4] J. Makó, Zs. Páles, Strengthening of strong and approximate convexity, Acta Math. Hungar. 132(1-2) (2011), 78–91.
• [5] A. Najdecki, Jacek Tabor, Józef Tabor, On conditionally δ-convex functions, Acta Math. Hungar. 128(1-2) (2010), 131–138.
• [6] C. Niculescu, L. E. Persson, Convex Functions and Their Applications, CMS Books in Mathematics, Springer, 2006.
• [7] H. J. M. Peters, P. P. Wakker, Convex functions on non-convex domains, Econom. Lett. 22 (1987), 251–255.
• [8] S. Rolewicz, On α(∙)-paraconvex and strongly α(∙)-paraconvex functions, Control Cybernet. 29 (2000), 367–377.
• [9] R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.