@article{Attia2024, 
author = {Najmeddine Attia and Taoufik Moulahi and Rim Amami and Neji Saidi},
title = {Note on fractal interpolation function with variable parameters},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {2},
pages = {2584-2601},
keywords = {iterated function system, generalized affine fractal interpolation function, hölder and Lipschitz functions},
url = {https://www.sciopen.com/article/10.3934/math.2024127},
doi = {10.3934/math.2024127},
abstract = {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        W    n    (  x  ,  y  )  =      (        a    n    x  +      e    n    ,      α    n    (  x  )  y  +      ψ    n    (  x  )      )  ,    n  =  1  ,  …  ,  N. Then, we may define the generalized affine FIF    f interpolating a given data set        {    (      x    n    ,      y    n    )  ∈  I  ×      R    ,  n  =  0  ,  1  ,  …  ,  N      }  , where    I  =  [      x    0    ,      x    N    ]. In this paper, we discuss the smoothness of the FIF    f. We prove, in particular, that    f is    θ-hölder function whenever        ψ    n   are. Furthermore, we give the appropriate upper bound of the maximum range of FIF in this case.}
}