Some Jensen's type inequalities for twice differentiable functions of selfadjoint operators in Hilbert spaces
نویسندگان
چکیده
منابع مشابه
Some Jensen’s Type Inequalities for Twice Differentiable Functions of Selfadjoint Operators in Hilbert Spaces
Some Jensen’s type inequalities for twice differentiable functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided.
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and Applied Analysis 3 where ‖ · ‖p p ∈ 1,∞ are the Lebesgue norms, that is, ∥∥f ′∥∞ ess sup s∈ a,b ∣∣f ′ s ∣∣, ∥∥f ′∥∥ p : (∫b a ∣∣f ′ s ∣∣ds)1/p, p ≥ 1. 1.6 The case of convex functions is as follows 4 . Theorem 1.5. Let f : a, b → be a convex function on a, b . Then one has the inequalities 1 8 b − a 2 [ f ′ ( a b 2 ) − f ′ − ( a b 2 )] ≤ f a f b 2 b − a − ∫b
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ژورنال
عنوان ژورنال: Filomat
سال: 2009
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil0903211d