EDB β€” 14D

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E25

[14D]Prerequisites:[2CS],[118].Let Cb=Cb(I) be the space of continuous bounded functions f:I:β†’R). This is a Banach space (a complete normed space) with the norm β€–fβ€–βˆž=supx|f(x)|.

Consider the map F:[0,∞)Γ—Cbβ†’Cb transforming g=F(Ξ΅,f), as defined in the eqn. [(12.20)].

Show that F is continuous.

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  • Banach, space
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