Approximation properties of bivariate α-fractal functions and dimension results. Issue 16 (10th December 2021) - Jha, Sangita; Chand, A. K. B.; Navascués, M. A.; Sahu, Abhilash
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.