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More General fractal functions on the Sphere

MEDITERRANEAN JOURNAL OF MATHEMATICS 2019年第6期16卷 134-134页

作者： Akhtar, Md. Nasim Guru Prem Prasad, M. Navascues, M. A. Indian Inst Technol Guwahati Dept Math Gauhati 781039 Assam India Univ Zaragoza Dept Matemat Aplicada Zaragoza Spain

In this article, a family of continuous functions on the unit sphere S subset of R-3 generalizing the spherical harmonics, is considered. Using fractal methodology, the fractal version of this family of continuous functions on the sphere S is constructed. To do this, an iterated function system (IFS) and a linear bounded operator that maps classical functions to its fractal analogues is defined. Some approximation properties of fractal functions on the sphere are investigated. Restricting the scale vector involved in the IFS, a fractal Hilbert basis is established for the functions on the sphere.

关键词： fractal interpolation functions alpha-fractal interpolation functions spherical harmonics best approximations Hilbert bases

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Box dimension of α-fractal function with variable scaling factors in subintervals

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CHAOS SOLITONS & fractalS 2017年 103卷 440-449页

作者： Akhtar, Md Nasim Prasad, M. Guru Prem Navascures, M. A. IIT Guwahati Dept Math Gauhati 781039 India Univ Zaragoza Dept Matemat Aplicada Zaragoza Spain

The box dimension of the graph of non-affine alpha-fractal interpolation function f(alpha) with variable scaling factors is estimated in the interval [0, 1]. Due to the non- affinity of f(alpha), the behavior of the graph is nonuniform in the subintervals. An attempt is made to estimate the box dimension of the graph of f(alpha) in the subintervals as well and it is compared with the box dimension of f(alpha) on the whole interval. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： fractal interpolation functions alpha-fractal interpolation functions Variable scaling factors Box-counting dimensions

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BOX DIMENSIONS OF α-fractal functions

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fractalS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 2016年第3期24卷 1650037-1650037页

作者： Akhtar, Md. Nasim Prasad, M. Guru Prem Navascues, M. A. Indian Inst Technol Guwahati Dept Math Gauhati 781039 Assam India Univ Zaragoza Dept Mate Aplicada E-50009 Zaragoza Spain

The box dimension of the graph of non-affine, continuous, nowhere differentiable function fa which is a fractal analogue of a continuous function f corresponding to a certain iterated function system (IFS), is investigated in the present paper. The estimates for box dimension of the graph of alpha-fractal function f(alpha) for equally spaced as well as arbitrary data sets are found.

关键词： fractal interpolation functions alpha-fractal interpolation functions Variation of Continuous functions Box-Counting Dimensions

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