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Let K be a nonempty, closed, and convex subset of a real reflexive Banach space E that has weakly continuous duality mapping (J_{phi}) for some gauge ϕ.
Suppose further that { y t } is bounded or ( F ( T ) ≠ ∅ ) and E is a reflexive Banach space having a weakly continuous duality mapping J φ for some gauge φ.
Corollary 2.5 Let E be a reflexive Banach space which has a weakly continuous duality mapping J φ for some gauge φ, and let C be a nonempty closed and convex subset of E. Let T : C → C be a continuous pseudo-contraction.
Theorem 2.2 Let E be a reflexive Banach space which has a weakly continuous duality mapping J φ for some gauge φ, and let C be a nonempty closed and convex subset of E. Let T : C → C be a continuous pseudo-contraction and f : C → C be a fixed bounded, continuous and strong pseudo-contraction with the coefficient k ∈ ( 0, 1 ).
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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