Jensen-Mercer inequality and its applications (CROSBI ID 537816)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
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.
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objavljeno
Podaci o matičnoj publikaciji
Podaci o skupu
38th Annual Iranian Mathematics Conference
ostalo
03.09.2007-06.09.2007
Zanjān, Iran