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Jensen-Mercer inequality and its applications (CROSBI ID 537816)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija

Matković, Anita ; Pečarić, Josip Jensen-Mercer inequality and its applications. 2007

Podaci o odgovornosti

Matković, Anita ; Pečarić, Josip

engleski

Jensen-Mercer inequality and its applications

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.

Jensen's inequality; convex functions; operator convex functions; P-convex functions; functions with nondecreasing increments; power means; quasi-arithmetic means

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Podaci o prilogu

2007.

nije evidentirano

objavljeno

Podaci o matičnoj publikaciji

Podaci o skupu

38th Annual Iranian Mathematics Conference

ostalo

03.09.2007-06.09.2007

Zanjān, Iran

Povezanost rada

Matematika