TY - JOUR
T1 - Note on fractal interpolation function with variable parameters
AU - Attia, Najmeddine
AU - Moulahi, Taoufik
AU - Amami, Rim
AU - Saidi, Neji
N1 - Publisher Copyright:
© 2024 the Author(s), licensee AIMS Press.
PY - 2024
Y1 - 2024
N2 - Fractal interpolation function (FIF) is a new method of constructing new data points within the range of a discrete set of known data points. Consider the iterated functional system defined through the functions (Formula Presented). Then, we may define the generalized affine FIF f interpolating a given data set (Formula Presented), where (Formula Presented). In this paper, we discuss the smoothness of the FIF f . We prove, in particular, that f is θ-hölder function whenever ψn are. Furthermore, we give the appropriate upper bound of the maximum range of FIF in this case.
AB - Fractal interpolation function (FIF) is a new method of constructing new data points within the range of a discrete set of known data points. Consider the iterated functional system defined through the functions (Formula Presented). Then, we may define the generalized affine FIF f interpolating a given data set (Formula Presented), where (Formula Presented). In this paper, we discuss the smoothness of the FIF f . We prove, in particular, that f is θ-hölder function whenever ψn are. Furthermore, we give the appropriate upper bound of the maximum range of FIF in this case.
KW - generalized affine fractal interpolation function
KW - hölder and Lipschitz functions
KW - iterated function system
UR - https://www.scopus.com/pages/publications/85180721066
U2 - 10.3934/math.2024127
DO - 10.3934/math.2024127
M3 - Article
AN - SCOPUS:85180721066
SN - 2473-6988
VL - 9
SP - 2584
EP - 2601
JO - AIMS Mathematics
JF - AIMS Mathematics
IS - 2
ER -