TY - JOUR
AU - Priyadarshi, Amit
AB - In this paper, we obtain a vector-valued fractal interpolation function in a more general setting by using the Rakotch fixed point theory and the iterated function system. We also show the existence of the Borel probability measure, widely known as a fractal measure, supported on the graph of this vector-valued fractal interpolation function. We obtain the Hausdorff dimension and the box-counting dimension of the graph of this more general fractal function using some function spaces. We obtain bounds for the fractal dimension of the graph of the Riemann-Liouville fractional integral of this fractal function. Using our techniques, we also calculate the fractal dimensions of the graphs of some fractal interpolation functions.
TI - Dimensions of new fractal functions and associated measures
JF - Numerical Algorithms
DO - 10.1007/s11075-023-01521-0
DA - 2023-10-01
UR - https://www.deepdyve.com/lp/springer-journals/dimensions-of-new-fractal-functions-and-associated-measures-LGqYYrHoXr
SP - 817
EP - 846
VL - 94
IS - 2
DP - DeepDyve
ER -