19 citations · 24 across the 10 of their papers we have counts for
10 papers
Katugampola fractional integral and fractal dimension of bivariate functions
S. Verma, P. Viswanathan
The subject of this note is the mixed Katugampola fractional integral of a bivariate function defined on a rectangular region in the Cartesian plane. This is a natural extension of…
On Bivariate Fractal Interpolation for Countable Data and Associated Nonlinear Fractal Operator
K. K. Pandey, P. Viswanathan
We provide a general framework to construct fractal interpolation surfaces (FISs) for a prescribed countably infinite data set on a rectangular grid. Using this as a crucial tool,…
Bivariate functions of bounded variation: Fractal dimension and fractional integral
S. Verma, P. Viswanathan
In contrast to the univariate case, several definitions are available for the notion of bounded variation for a bivariate function. This article is an attempt to study the Hausdorf…
A fractalization of rational trigonometric function
S. Verma, P. Viswanathan
In [14,26], new approximation classes of self-referential functions are introduced as fractal versions of the classes of polynomials and rational functions. As a sequel, in the pre…
A fractal operator associated to bivariate fractal interpolation functions
S. Verma, P. Viswanathan
A general framework to construct fractal interpolation surfaces (FISs) on rectangular grids was presented and bilinear FIS was deduced by Ruan and Xu [Bull. Aust. Math. Soc. 91(3),…
A Fractal Operator on Some Standard Spaces of Functions
P. Viswanathan, M. A. Navascues
By appropriate choices of elements in the underlying iterated function system, methodology of fractal interpolation entitles one to associate a family of continuous self-referentia…