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
Zanjān, Iran, 03.09.2007. - 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