A fractal class of generalized Jackson interpolants. Issue 5 (1st August 2019) - Navascués, María Antonia; Jha, Sangita; Chand, A.K.B.; Sebastián, María Victoria
Abstract : In this paper, we establish a new formula that generalizes the Jackson trigonometric interpolation for a 2 π ‐periodic function. This generalization is done by using various positive exponents in the basic nodal functions that gives a wide variety of bases during approximation. For a Hölder continuous periodic function, we compute the uniform interpolation error bound of the corresponding generalized Jackson interpolant and prove the convergence of the proposed interpolant. We also show that the mentioned approximation procedure is stable. In the last part, we consider a family of fractal interpolants associated with the generalized Jackson approximation functions under discussion.