ON THE CLASSICAL INTEGRAL OF FRACTAL FUNCTIONS

T. M. C. Priyanka (), C. Serpa () and A. Gowrisankar
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T. M. C. Priyanka: Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632 014, Tamil Nadu, India
C. Serpa: ISEL - Instituto Superior de Engenharia de Lisboa, Centro de Matemática Aplicações Fundamentais e Investigação Operacional, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisbon, Portugal
A. Gowrisankar: Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632 014, Tamil Nadu, India

FRACTALS (fractals), 2023, vol. 31, issue 05, 1-20

Abstract: In this paper, the integral of classical fractal interpolation function (FIF) and A-fractal function is explored for both the cases of constant and variable scaling factors. The definite integral for the classical FIF in the closed interval of â„ is estimated. The novel notion of affine-quadratic FIF is introduced and integrated for both constant and variable scaling factors. It is demonstrated that its integral is not an affine-quadratic FIF, however it is a FIF. Similarly, by choosing the vertical scaling factors as constants and variables, A-fractal function is integrated. Further, by assuming certain condition on the block matrix, it is shown that like the original A-fractal function its integral is also an attractor for the iterated function system.

Keywords: Fractal Interpolation Function; Classical Integral; Constant Scaling Factors; Variable Scaling Factors (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500573

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