منابع مشابه
Inequalities of Jensen-pečarić-svrtan-fan Type
By using the theory of majorization, the following inequalities of Jensen-PečarićSvrtan-Fan type are established: Let I be an interval, f : I → R and t ∈ I, x, a, b ∈ I. If a1 ≤ · · · ≤ an ≤ bn ≤ · · · ≤ b1, a1 +b1 ≤ · · · ≤ an +bn; f(t) > 0, f ′(t) > 0, f ′′(t) > 0, f ′′′(t) < 0 for any t ∈ I, then f(A(a)) f(A(b)) = fn,n(a) fn,n(b) ≤ · · · ≤ fk+1,n(a) fk+1,n(b) ≤ fk,n(a) fk,n(b) ≤ · · · ≤ f1,n...
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We give further improvements of the Jensen inequality and its converse on time scales, allowing also negative weights. These results generalize the Jensen inequality and its converse for both discrete and continuous cases. Further, we investigate the exponential and logarithmic convexity of the differences between the left-hand side and the right-hand side of these inequalities and present seve...
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In this paper, we provide inequalities of Jensen-Ostrowski type, by investigating the magnitude of the quantity ∫ Ω (f ◦ g) dμ− f(ζ)− ∫ Ω (g − ζ)f ′ ◦ g dμ+ 1 2 λ ∫ Ω (g − ζ) dμ, for various assumptions on the absolutely continuous function f : [a, b] → C, ζ ∈ [a, b], λ ∈ C and a μ-measurable function g on Ω. Special cases are considered to provide some inequalities of Jensen type, as well as O...
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ژورنال
عنوان ژورنال: Topological Algebra and its Applications
سال: 2013
ISSN: 2299-3231
DOI: 10.2478/taa-2013-0002