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Theoretically, the projection is easier for calculating than the generalized projection in a general Banach space since the generalized projection involves a Lyapunov functional.
They proved that the sequence generated by the above algorithm converges strongly to, where is the generalized projection of onto.
The generalized projection defined by.
The generalized projection mapping above is relatively nonexpansive and.
Concerning the generalized projection, the following are well known.
Moreover, (x_{0}) is called the generalized projection of x.
Alber's generalized projection is an example of relatively nonexpansive mappings.
The mapping is called the generalized projection from onto.
Following Alber [21], the generalized projection is defined by.
where is the duality mapping on, and is the generalized projection of onto.
The generalized projection from onto is well defined, single valued and satisfies.
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