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We investigate the Weyl-Wigner-Gr\"oenewold-Moyal, the Stratonovich and theBerezin group quantization schemes for the space-space noncommutativeHeisenberg-Weyl group. We show that the $\star$-product for the deformedalgebra of Weyl functions for the first scheme is different than that for theother two, even though their respective quantum mechanics' are equivalent asfar as expectation values are concerned, provided that some additional criteriaare imposed on the implementation of this process. We also show that it is the$\star$-product associated with the Stratonovich and the Berezin formalismsthat correctly gives the Weyl symbol of a product of operators in terms of thedeformed product of their corresponding Weyl symbols. To conclude, we derivethe stronger $\star$-valued equations for the 3 quantization schemes consideredand discuss the criteria that are also needed for them to exist.

On deformed quantum mechanical schemes and $\star$-value equations based on the space-space noncommutative Heisenberg-Weyl group