A fractal class of generalized Jackson interpolants. Issue 5 (1st August 2019)

• Record Type: Journal Article
• Authors: Navascués, María Antonia; Jha, Sangita; Chand, A.K.B.; Sebastián, María Victoria
• Is Part Of: Computational and mathematical methods. Volume 1:Issue 5(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-08-01
• Subjects: curve fitting -- fractals -- Jackson interpolation -- smoothing -- trigonometric interpolation; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1054
• Languages: English
• ISSNs: 2577-7408

Abstract

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.