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- W3191553292 abstract "Let f be an operator convex function on I and A,B ϵ SAI(H), the convex set of selfadjoint operators with spectra in I. If A≠B and f, as an operator function, is Gâteaux differentiable on [ A,B ] := { (1−t)A+tB|t∈[ 0,1 ] }, while p : [ 0,1 ]→[0, ∞) is Lebesgue integrable satisfying the condition 0≤∫0τp(s)ds≤∫01p(s)ds for all τ∈[0,1] and symmetric, namely p(1−t) =p(t) for all tϵ [ 0, 1 ] then −1∫01p(τ)dτ∫01(∫0τp(s)ds)(1−τ)dτ[∇fB(B−A)−∇fA(B−A)]≤1∫01p(τ)dτ∫01p(τ)f((1−τ)A+τB)dτ−∫01f((1−τ)A+τB)dτ≤1∫01p(τ)dτ∫01(∫0τp(s)ds)(1−τ)dτ[∇fB(B−A)−∇fA(B−A)]. Some particular examples of interest are also given." @default.
- W3191553292 created "2021-08-16" @default.
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- W3191553292 date "2020-12-01" @default.
- W3191553292 modified "2023-10-17" @default.
- W3191553292 title "Some inequalities for weighted and integral means of operator convex functions" @default.
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- W3191553292 doi "https://doi.org/10.55937/sut/1609966712" @default.
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