Work

Shape Preserving Approximation of Periodic Functions: Conclusion

Year: 2024

Type: article

Abstract: We give here the final results about the validity of Jackson-type estimates in comonotone approximation of $$2\pi $$ 2 π -periodic functions by trigonometric polynomials ( $$q=1$$ q = 1 ). For coconvex ( $$q=2$$ q = 2 ) and the so called co- q -monotone, $$q>2$$ q > 2 , approximations, everything is known by now. Thus, this paper concludes the research on Jackson type estimates of Shape Preserving Approximation of periodic functions by trigonometric polynomials. It is interesting to point out that the results for comonotone approximation of a periodic function are substantially different than the analogous results for comonotone approximation of a continuous function on a finite interval, by algebraic polynomials.

Source: Constructive Approximation

DOI: 10.1007/s00365-024-09695-z

Authors: D. Leviatan, I. O. Shevchuk

Institutions: Tel Aviv University, Taras Shevchenko National University of Kyiv

Language: English

Topic: Approximation Theory and Sequence Spaces

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Tel Aviv University