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The mapping on many is bigger than usual, offering alternative routes and ways to achieve objectives.
Define the mapping on by.
Define a mapping on by (5.2).
Consequently, is a self mapping on.
and define a mapping on by (1.12).
Define a mapping on by, and for.
Let be a mapping on a set.
Let be the identity mapping on.
where is a set-valued mapping on.
Let be a multivalued mapping on.
where is the duality mapping on.
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