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reverses of the first hermite-hadamard type inequality for the square operator modulus in hilbert spaces
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نویسنده
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dragomir s. s.
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منبع
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journal of linear and topological algebra - 2022 - دوره : 11 - شماره : 1 - صفحه:1 -13
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چکیده
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let (h;⟨⋅,⋅⟩) be a complex hilbert space. denote by b(h) b(h) the banach c^∗ -algebra of bounded linear operators on h . for a∈b(h) we define the modulus of a by |a|:=(a∗a)1/2 and funcrea:=12(a∗+a). . in this paper we show among other that, if a, b∈b(h) with 0≤m≤|(1−t)a+tb|^2≤m for all t∈[0,1], then 0≤∫1_0f(|(1−t)a+tb|2)dt−f(|a|2+funcre(b∗a)+|b|23)≤2[f(m)+f(m)2−f(m+m2)]1h for operator convex functions f:[0,∞)→r . applications for power and logarithmic functions are also provided
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کلیدواژه
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operator convex functions ,hermite-hadamard inequality ,midpoint inequality ,operator power and logarithmic functions
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آدرس
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victoria university, college of engineering & science, australia. university of the witwatersrand, dst-nrf centre of excellence in the mathematical and statistical sciences, school of computer science & applied mathematics, south africa
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پست الکترونیکی
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sever.dragomir@vu.edu.au
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Authors
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