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Pregled bibliografske jedinice broj: 445180

Zbornik radova

Autori: Banić, Senka
Naslov: On refining of inequalities for convex functions by the concept of superquadracity
( On refining of inequalities for convex functions by the concept of superquadracity )
Izvornik: International Congress on Mathematics MICOM 2009, Book of Abstracts / Dodunekov, Stefan ; Eraković, Vesna (ur.). - Skopje : Union of Mathematicans of Macedonia , 2009. 14-14.
Skup: MASSEE International Congress on Mathematics MICOM 2009
Mjesto i datum: Ohrid, Makedonija, 16-20.09.2009.
Ključne riječi: convex functions; superquadratic functions; Jensen's inequality; Hölder's inequality; Slater's inequality; Hermite-Hadamard inequalities
( convex functions; superquadratic functions; Jensen's inequality; Hölder's inequality; Slater's inequality; Hermite-Hadamard inequalities )
Sažetak:
In 2004 S. Abramovich, G. Jameson and G. Sinnamon introduced a new interesting class of functions: the class of superquadratic functions. We say that the function ϕ is superquadratic if for any x≥0 there exists C(x)∈R such that ϕ(y)≥ϕ(x)+C(x)(y-x)+ϕ(|y-x|), ∀y≥0. In 2007 S. Abramovich, S. Banić and M. Matić generalized this concept for the functions in several variables. The class of superquadratic functions is strongly related to the class of convex functions: it can be proved that any nonnegative superquadratic function is convex. Using some previously proved characterizations and properties of this new class we establish "superquadratic variants" of several well known inequalities for convex functions. The refinements of many important inequalities for convex functions easily follow as special cases when considered superquadratic functions are nonnegative.
Vrsta sudjelovanja: Predavanje
Vrsta prezentacije u zborniku: Sažetak
Vrsta recenzije: Međunarodna recenzija
Projekt / tema: 177-1170889-1287
Izvorni jezik: eng
Kategorija: Znanstveni
Znanstvena područja:
Matematika
Upisao u CROSBI: senka@gradst.hr (senka@gradst.hr), 20. Vel. 2010. u 20:23 sati



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