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Jensen-Mercer inequality and its applications


Matković, Anita; Pečarić, Josip
Jensen-Mercer inequality and its applications // 38th Annual Iranian Mathematics Conference
Zanjan, Iran, 2007. (plenarno, međunarodna recenzija, sažetak, znanstveni)


Naslov
Jensen-Mercer inequality and its applications

Autori
Matković, Anita ; Pečarić, Josip

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Skup
38th Annual Iranian Mathematics Conference

Mjesto i datum
Zanjan, Iran, 03-06. 09. 2007

Vrsta sudjelovanja
Plenarno

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekt / tema
117-1170889-0888 - Generalne nejednakosti i primjene (Josip Pečarić, )
177-1170889-1287 - Konveksne funkcije i primjene (Marko Matić, )

Ustanove
Fakultet elektrotehnike, strojarstva i brodogradnje, Split,
Tekstilno-tehnološki fakultet, Zagreb,
Prirodoslovno-matematički fakultet, Split