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Fack and Kosaki [2] investigated generalized s-numbers of τ-measurable operators and proved dominated convergence theorems for a gage and convexity (or concavity) inequality.
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They are the people who intimidate just to prove dominating.
In order to prove the dominated convergence result we need to relate the distances (bar{d}_0) and (bar{d}_epsilon ).
This paper presents a new approach for exactly solving the Unbounded Knapsack Problem (UKP) and proposes a new bound that was proved to dominate the previous bounds on a special class of UKP instances.
Prosecutors have relied on the evidence against Mr. Malvo in their effort to prove that Mr. Muhammad dominated, even controlled him.
And so it proved - the Shrews dominated David Moyes's side for long periods and could perhaps have won by a bigger margin, if not for the heroics of Richard Wright in the Everton goal.
Both sides played with passion and intensity but Nigeria's hunger - they still have a chance to qualify for the Olympics - proved decisive and they dominated the extra period.
In order to prove statement (2) of the lemma, it suffices to verify that the function s↦D s,x), s∈[t 0,t], is continuous, a fact that can be proved using Lebesgue's dominated convergence theorem.
Remark 1 If function φ is the identity in (2.4) and (2.5), then they reduce to Hermite-Hadamard type inequalities for convex dominated functions proved by Dragomir, Pearce and Pečarić in [2].
Remark 2 If function φ is the identity in (2.6) and (2.7), then they reduce to Hermite-Hadamard type inequalities for ( g, s ) -convex dominated functions proved by Kavurmacı, Özdemir and Sarıkaya in [4].
Remark 3 If function φ is the identity in (2.8), then it reduces to Hermite-Hadamard type inequality for ( g, Q ( I ) ) -convex dominated functions proved by Özdemir, Tunç and Kavurmacı in [6].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com