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Then from (15), for any 0 < a < b < ∞, there exists 0 < γ ( a, b ) < 1 such that for all x, y ∈ X, Now, T satisfies condition (2) of Theorem 2.1 with d = p s. Finally, to apply Theorem 2.1, we have to check the lower semi-continuity of the function φ (with respect to the topology of p s ).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com