On the $q$-deformed oscillator algebras:$su_q(1,1)$ and $su_q(2)$

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Abstract: We study the relations between

q

-deformations and

q

-coherent states of the single oscillator representations for

s u_{q} (1, 1)

and

s u_{q} (2)

algebras; Dyson and Holstein-Primakoff type in terms of Biedenharn, Macfarlane and anyonic oscilators. We also discuss the related Fock-Bargmann

q

-derivative and integration.

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