Fractals, Wavelets, and their Applications by Christoph Bandt Michael Barnsley Robert Devaney Kenneth J. Falconer V. Kannan & Vinod Kumar P.B

Author:Christoph Bandt, Michael Barnsley, Robert Devaney, Kenneth J. Falconer, V. Kannan & Vinod Kumar P.B.
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Now suppose that is an F-space. Denote its metric by . We define mappings by

(8)

where and is a function.

If in addition we require that the metric is homogeneous, that is,

then v i given by (8) satisfies condition (5) provided that the functions S i are bounded on X i with bounds in [0, 1). For then

Here, we denoted the supremum norm with respect to X i by , and set .

Thus, for a fixed set of functions {λ 1, …, λ N } and {S 1, …, S N }, the associated RB operator (6) has now the form

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