Abstract Recently, deformed quantum systems have received lots of attention in the literature. Dunkl formalism differs from others by containing difference-differential and reflection operator. It is one most interesting deformations since it let us discuss solutions according to even odd solutions. In this work, we studied ideal Bose gas blackbody radiation via formalism. To end, made a liaiso...

In this paper, three-dimensional Dunkl oscillator models are studied in a generalized form of superintegrable Euclidean Hamiltonian systems to curved ones. These defined based on Hamiltonians, which depend deformation parameter underlying space and involve reflection operators. The corresponding symmetries obtained by the Jordan–Schwinger representations family Cayley–Klein orthogonal algebras ...

In this paper, several direct and inverse theorems in terms of the best approximations functions moduli smoothness are proved concerning approximation from space $$\mathbb {L}_{2}^{(\alpha ,\beta )}$$ by partial sums Jacobi-Dunkl series. For purpose, we use generalized translation operator which was defined Vinogradov.