Based on the combination of fractional calculus with fractal functions, a new type of functions is introduced; the definition, graph, property and dimension of this function are discussed.
The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The exact box dimension for such functions many important cases is established. We need to point out that, althoug...The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The exact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.展开更多
This paper gives the weighted Lp convergence rate estimations of the Grunwald interpolatory polynomials based on the zeros of Chebyshev polynomials of the first kind, and proves that the order of the estimations is op...This paper gives the weighted Lp convergence rate estimations of the Grunwald interpolatory polynomials based on the zeros of Chebyshev polynomials of the first kind, and proves that the order of the estimations is optimal for p≥1.展开更多
基金National Natural Science Foundation of Zhejiang Province
文摘Based on the combination of fractional calculus with fractal functions, a new type of functions is introduced; the definition, graph, property and dimension of this function are discussed.
文摘The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The exact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.
文摘This paper gives the weighted Lp convergence rate estimations of the Grunwald interpolatory polynomials based on the zeros of Chebyshev polynomials of the first kind, and proves that the order of the estimations is optimal for p≥1.
