Fejér-type inequalities for strongly convex functions
Abstract
Fejér-type inequalities as well as some refinement and a discrete version of the Hermite–Hadamard inequalities for strongly convex functions are presented.
Keywords
strongly convex functions; Hermite–Hadamard inequalities; Fejér inequalities
References
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16. Rajba T., Wąsowicz Sz., Probabilistic characterization of strong convexity, Opuscula Math. 31 (2011), no. 1, 97–103.
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2. Bessenyei M., Páles Zs., Characterization of convexity via Hadamard’s inequality, Math. Inequal. Appl. 9 (2006), no. 1, 53–62.
3. Dragomir S.S., Pearce C.E.M., Selected Topics on Hermite–Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2002. (online: http://rgmia.vu.edu.au/monographs/).
4. Fejér L., Über die Fourierreihen, II, Math. Naturwiss, Anz. Ungar. Akad. Wiss. 24 (1906), 369–390 (in Hungarian).
5. Hadamard J., Étude sur les propriétés entières et en particulier d’une fonction considerée par Riemann, J. Math. Pures Appl. 58 (1893), 171–215.
6. Hermite Ch., Sur deux limites d’une intégrale définie, Mathesis 3 (1883), 82.
7. Hiriart–Urruty J.-B., Lemaréchal C., Fundamentals of Convex Analysis, Springer- Verlag, Berlin–Heidelberg, 2001.
8. Jovanovič M.V., A note on strongly convex and strongly quasiconvex functions, Math. Notes 60 (1996), no. 5, 778–779.
9. Kuczma M., An Introduction to the Theory of Functional Equations and Inequalities. Cauchy’s Equation and Jensen’s Inequality, PWN – Uniwersytet Śląski, Warszawa– Kraków–Katowice, 1985. Second Edition: Birkhäuser, Basel–Boston–Berlin, 2009.
10. Merentes N., Nikodem K., Remarks on strongly convex functions, Aequationes Math. 80 (2010), 193–199.
11. Niculescu C.P., Persson L.-E., Convex Functions and their Applications. A Contemporary Approach, CMS Books in Mathematics, vol. 23, Springer, New York, 2006.
12. Nikodem K., Páles Zs., Characterizations of inner product spaces by strongly convex functions, Banach J. Math. Anal. 5 (2011), no. 1, 83–87.
13. Pečarić J.E., On some inequalities for convex functions and some related applications, Mat. Bilten (Skopje) 5–6 (1981–1982), 29–36.
14. Pečarić J.E., Proschan F., Tong Y.L., Convex Functions, Partial Orderings, and Statistical Applications, Academic Press, Boston, 1992.
15. Polyak B.T., Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl. 7 (1966), 72–75.
16. Rajba T., Wąsowicz Sz., Probabilistic characterization of strong convexity, Opuscula Math. 31 (2011), no. 1, 97–103.
17. Roberts A.W., Varberg D.E., Convex Functions, Academic Press, New York–London, 1973.
18. Vial J.P., Strong convexity of sets and functions, J. Math. Economy 9 (1982), 187–205.
19. Vial J.P., Strong and weak convexity of sets and functions, Math. Oper. Res. 8 (1983), 231–259.
20. Zalinescu C., Convex Analysis in General Vector Spaces, World Scientific, New Jersey, 2002.
AzócarA., NikodemK., & RoaG. (2013). Fejér-type inequalities for strongly convex functions. Annales Mathematicae Silesianae, 26, 43-54. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14012
Antonio Azócar
Departamento de Matemáticas, Universidad Nacional Abierta, Venezuela Venezuela, Bolivarian Republic of
Departamento de Matemáticas, Universidad Nacional Abierta, Venezuela Venezuela, Bolivarian Republic of
Kazimierz Nikodem
knikodem@ath.bielsko.pl
Katedra Matematyki i Informatyki, Akademia Techniczno-Humanistyczna w Bielsku-Białej Poland
Katedra Matematyki i Informatyki, Akademia Techniczno-Humanistyczna w Bielsku-Białej Poland
Gari Roa
Escuela de Matemáticas, Universidad Central de Venezuela Venezuela, Bolivarian Republic of
Escuela de Matemáticas, Universidad Central de Venezuela Venezuela, Bolivarian Republic of
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