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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

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}; ; ))&#8721; _{; ; i=1}; ; &#8319; w_{; ; i}; ; x_{; ; i}; ; )&#8804; f(a)+f(b)-(1/(W_{; ; n}; ; ))&#8721; _{; ; i=1}; ; &#8319; w_{; ; i}; ; f(x_{; ; i}; ; ), for convex function f:[a, b]&#8594; &#8477; , real numbers x&#8321; , &#8230; , x_{; ; n}; ; &#8712; [a, b] and positive real numbers w&#8321; , &#8230; , w_{; ; n}; ; , where W_{; ; n}; ; =&#8721; _{; ; i=1}; ; &#8319; 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