Abstract
Using general construction of star-product the q-deformed Wigner–Weyl–Moyal quantization procedure is elaborated. The q-deformed Groenewold kernel determining the product of quantum observables is given in explicit form for small nonlinearities corresponding to nonlinear vibrations of classical and quantum q-oscillators. The deformation of Groenewold kernel related to general kinds of nonlinear vibrations described by f-oscillators are considered.
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