Local α-fractal interpolation function

Constructions of the (global) fractal interpolation functions on standard function spaces got a lot of attention in the last centuries. Motivated by the newly introduced local fractal functions corresponding to a local iterated functions system which is the generalization of the traditional iterated...

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Published inThe European physical journal. ST, Special topics Vol. 232; no. 7; pp. 1043 - 1050
Main Authors Banerjee, Akash, Akhtar, Md. Nasim, Navascués, M. A.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2023
Springer Nature B.V
Subjects
Atomic
Classical and Continuum Physics
Condensed Matter Physics
Fractals
Framework of Fractals in Data Analysis: Theory and Interpretation
Function space
Interpolation
Materials Science
Measurement Science and Instrumentation
Molecular
Operators (mathematics)
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
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Summary:Constructions of the (global) fractal interpolation functions on standard function spaces got a lot of attention in the last centuries. Motivated by the newly introduced local fractal functions corresponding to a local iterated functions system which is the generalization of the traditional iterated functions system we construct the local non-affine α - fractal functions in this article. A few examples of the graphs of these functions are provided. A fractal operator which takes the classical function to its local fractal counterpart is defined and some of its properties are also studied.
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ISSN:1951-6355
1951-6401
DOI:10.1140/epjs/s11734-023-00865-x