On refining of inequalities for convex functions by the concept of superquadracity (CROSBI ID 558686)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Banić, Senka
engleski
On refining of inequalities for convex functions by the concept of superquadracity
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.
convex functions; superquadratic functions; Jensen's inequality; Hölder's inequality; Slater's inequality; Hermite-Hadamard inequalities
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Podaci o prilogu
14-14.
2009.
objavljeno
Podaci o matičnoj publikaciji
International Congress on Mathematics MICOM 2009, Book of Abstracts
Dodunekov, Stefan ; Eraković, Vesna
Skopje: Union of Mathematicans of Macedonia
Podaci o skupu
MASSEE International Congress on Mathematics MICOM 2009
predavanje
16.09.2009-20.09.2009
Skopje, Sjeverna Makedonija