Approximation properties of bivariate α-fractal functions and dimension results

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 (Formula presented.) and the Lebesgue space (Formula presented.). Also, we study some approximation properties using bivariate Bernstein α-fractal trigonometric functions.