Fractal Quintic Spline Solutions for Fourth-Order Boundary-Value Problems

Balasubramani, N.; Prasad, M. G.; Natesan, Srinivasan

doi:10.1007/s40819-019-0715-y

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…where the maps l n are homeomorphisms, W n are continuous and both satisfy the join-up conditions (1), (2). We have proved that for maps W n of type W n (x, y) = U n (x) + R n (y), or W n (x, y) = U n (x) + R n (x, y), where U n is continuous and R n is a Matkowski contraction, or a Matkowski contraction in the second variable, respectively, the IFS defines a continuous FIF interpolating the data.…”

Section: Discussionmentioning

confidence: 99%

“…The concept of a fractal interpolation function, or FIF for short, introduced by Barnsley in [1] gained a lot of attention from researchers and has been intensively studied in recent years; see, for instance, [2][3][4][5][6][7][8][9]. The interest in this type of interpolation is motivated by the significant applicability of fractal interpolation to model real-life data.…”

Section: Introductionmentioning

confidence: 99%

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Scale-Free Fractal Interpolation

2022

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An iterated function system that defines a fractal interpolation function, where ordinate scaling is replaced by a nonlinear contraction, is investigated here. In such a manner, fractal interpolation functions associated with Matkowski contractions for finite as well as infinite (countable) sets of data are obtained. Furthermore, we construct an extension of the concept of α-fractal interpolation functions, herein called R-fractal interpolation functions, related to a finite as well as to a countable iterated function system and provide approximation properties of the R-fractal functions. Moreover, we obtain smooth R-fractal interpolation functions and provide results that ensure the existence of differentiable R-fractal interpolation functions both for the finite and the infinite (countable) cases.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scale-Free Fractal Interpolation

2022

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“…In this way, the field of Approximation Theory has been considerably enriched with different models. The contributions in the area of fractal interpolation are recent and numerous, both in theory as well as in applications (see, for instance, [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]).…”

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confidence: 99%

Fractal Curves on Banach Algebras

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2022

Fractal Fract

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Most of the fractal functions studied so far run through numerical values. Usually they are supported on sets of real numbers or in a complex field. This paper is devoted to the construction of fractal curves with values in abstract settings such as Banach spaces and algebras, with minimal conditions and structures, transcending in this way the numerical underlying scenario. This is performed via fixed point of an operator defined on a b-metric space of Banach-valued functions with domain on a real interval. The sets of images may provide uniparametric fractal collections of measures, operators or matrices, for instance. The defining operator is linked to a collection of maps (or iterated function system, and the conditions on these mappings determine the properties of the fractal function. In particular, it is possible to define continuous curves and fractal functions belonging to Bochner spaces of Banach-valued integrable functions. As residual result, we prove the existence of fractal functions coming from non-contractive operators as well. We provide new constructions of bases for Banach-valued maps, with a particular mention of spanning systems of functions valued on C*-algebras.

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