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Pregled bibliografske jedinice broj: 348842

Zbornik radova

Autori: Matković, Anita; Pečarić, Josip
Naslov: Jensen-Mercer inequality and its applications
( Jensen-Mercer inequality and its applications )
Izvornik:
Skup: 38th Annual Iranian Mathematics Conference
Mjesto i datum: Zanjan, Iran, 03-06. 09. 2007.
Ključne riječi: Jensen's inequality; convex functions; operator convex functions; P-convex functions; functions with nondecreasing increments; power means; quasi-arithmetic means
( Jensen's inequality; convex functions; operator convex functions; P-convex functions; functions with nondecreasing increments; power means; quasi-arithmetic means )
Sažetak:
Our starting point is the following variant of Jensen's inequality f(a+b-(1/(W_{; ; n}; ; ))∑ _{; ; i=1}; ; ⁿ w_{; ; i}; ; x_{; ; i}; ; )≤ f(a)+f(b)-(1/(W_{; ; n}; ; ))∑ _{; ; i=1}; ; ⁿ w_{; ; i}; ; f(x_{; ; i}; ; ), for convex function f:[a, b]→ ℝ , real numbers x₁ , … , x_{; ; n}; ; ∈ [a, b] and positive real numbers w₁ , … , w_{; ; n}; ; , where W_{; ; n}; ; =∑ _{; ; i=1}; ; ⁿ w_{; ; i}; ; . We call it Jensen-Mercer inequality and we study its generalizations and refinements in various spaces with adequate orders, and for several types real valued functions. This enables us to define a variety of weighted means and to explore their relationships. We also present "Mercer's type" variants of several other well-known inequalities.
Vrsta sudjelovanja: Plenarno
Vrsta prezentacije u zborniku: Sažetak
Vrsta recenzije: Međunarodna recenzija
Projekt / tema: 117-1170889-0888, 177-1170889-1287
Izvorni jezik: eng
Kategorija: Znanstveni
Znanstvena područja:
Matematika
Upisao u CROSBI: anita@pmfst.hr (anita@pmfst.hr), 10. Svi. 2008. u 20:43 sati



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