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When a K i, let i max be the largest i satisfying a i ≥b i.
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for all x ∈ X and i ∈ I. Now weshow that T i = T j for any i,j ∈ I. Let i andj be two arbitrary fixed indexes of I. So, from lastinequality, we obtain ∥ f ( ρ i n ( x ) ) − P i, n ( x ) f ( x ) ∥ ≤ | P i, n ( x ) | θ i, n ( x ) ; Open image in new window (3.3) ∥ f ( ρ j n ( x ) ) − P j, n ( x ) f ( x ) ∥ ≤ | P j, n ( x ) | θ j, n ( x ) Open image in new window (3.4).
Let I = I δ.
Let i ∈ I be fixed.
Example 2. Let I = I u.
Now, let I ′ = I 1 ∩ I, we distinguish three cases.
(mbox{(i }Rightarrowmbox{(ii)}): Let (i) be valid.
Example 3. Consider the sequence space (c I ) F (M), and let I = I δ.
Let I ⊂ R +, φ : I → R + be continuous.
Let i ∈ I. Then x i = c i + T i xi-1.
Let I be any index set and let ({U_{i}}_{iin I}subsetmathcal {T}_{p}).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com