In this paper‎, ‎using a generalized Dunkl translation operator‎, ‎we obtain a generalization of Titchmarsh's Theorem for the Dunkl transform for functions satisfying the$(psi,p)$-Lipschitz Dunkl condition in the space $mathrm{L}_{p,alpha}=mathrm{L}^{p}(mathbb{R},|x|^{2alpha+1}dx)$‎, ‎where $alpha>-frac{1}{2}$.  

Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.

In this paper, $(p,q)$-Lupas Bernstein Stancu operators are constructed. Statistical as well as other approximation properties of $(p,q)$-Lupac{s} Stancu operators are studied. Rate of statistical convergence by means of modulus of continuity and Lipschitz type maximal functions has been investigated.

using a generalized spherical mean operator, we obtain the generalizationof titchmarsh's theorem for the dunkl transform for functions satisfyingthe lipschitz condition in l2(rd;wk), where wk is a weight function invariantunder the action of an associated reection groups.

Given any positive integers m and d, we say the a sequence of points (xi)i∈I in Rm is Lipschitz-d-controlling if one can select suitable values yi (i ∈ I) such that for every Lipschitz function f : Rm → Rd there exists i with |f(xi)−yi| < 1. We conjecture that for every m ≤ d, a sequence (xi)i∈I ⊂ Rm is d-controlling if and only if sup n∈N |{i ∈ I : |xi| ≤ n}| nd =∞. We prove that this conditio...

In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.