TY - Type of reference
TI - Approximation of Complex-Valued Functions by Fractal Functions
AU - N. Vijender
AB - Fractal approximants developed through iterated function systems (IFS) prove more versatile than classical approximants. In this paper, we introduce a new class of fractal approximants using the suitable bounded linear operators defined on the space C(I) of continuous functions and concept of $$$\alpha$$$-fractal functions. The convergence of the proposed fractal approximants towards the original continuous function does not need any condition on the scaling factors. The fractal approximants proposed in this paper possess fractality and convergence simultaneously. Without imposing any condition on the scaling vector, we establish the constrained approximation by the proposed fractal approximants. Existence of Schauder basis of fractal polynomials for the space of continuous functions C(I) is investigated. Using the proposed class of fractal approximants, we develop complex fractal approximants for representation of the square integrable complex-valued functions defined on a real compact interval.
DO - 10.21494/ISTE.OP.2021.0645
JF - Advances in Pure and Applied Mathematics
KW - Fractal approximation, Complex fractal approximation, Fractal dimension, Constrained fractal approximation, convergence, Fractal approximation, Complex fractal approximation, Fractal dimension, Constrained fractal approximation, convergence,
L1 - https://www.openscience.fr/IMG/pdf/iste_apam21v12n2_1.pdf
LA - en
PB - ISTE OpenScience
DA - 2021/04/26
SN - 1869-6090
TT - Approximation des fonctions à valeur complexe par les fonctions fractales
UR - https://www.openscience.fr/Approximation-of-Complex-Valued-Functions-by-Fractal-Functions
IS - Issue 2 (May 2021)
VL - 12
ER -