Approximation properties of bivariate α-fractal functions and dimension results. Issue 16 (10th December 2021)

• Record Type: Journal Article
• Authors: Jha, Sangita; Chand, A. K. B.; Navascués, M. A.; Sahu, Abhilash
• Is Part Of: Applicable analysis. Volume 100:Issue 16(2021)
• Page Start: 3426
• Page End: 3444
• Publication Date: 2021-12-10
• Subjects: Fractal function -- box dimension -- convergence -- function space -- trigonometric approximation; 28A80 -- 46B25 -- 42A15 -- 42A20 -- 65T40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1721472
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we study a different class of bivariate α -fractal functions. First, we introduce the bivariate Bernstein α -fractal functions that are more suitable to approximate both smooth and non-smooth surfaces and investigate their convergence properties. Then, we compute the box-counting dimension of the graph of the bivariate α -fractal functions for equally spaced data set. In regard to the connection of functional analysis and fractal function, we cogitate the bivariate fractal operator in spaces of functions such as k -times continuously differentiable functions space C k ( I × J ) and the Lebesgue space L p ( I × J ) . Also, we study some approximation properties using bivariate Bernstein α -fractal trigonometric functions.