Nonlinear approximation in N-dimension with the help of summability methods

Aslan, İsmail; Duman, Oktay

doi:10.1007/s13398-021-01046-y

Cited by 4 publications

(3 citation statements)

References 35 publications

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“…In the present paper, our purpose is to get approximations to the fractals which can be obtained as a fixed point of an IFS. For this approximation, inspired by the papers [1,[3][4][5], we construct non-affine contraction mappings. As is known, most of the fractals such as Sierpinski triangle, Sierpinski carpet, Sierpinski tetrahedron, Vicsek fractal and Koch curve can be obtained as the attractor of an iterated function systems.…”

Section: Introductionmentioning

confidence: 99%

“…For this purpose, firstly, the sequences of non-affine contraction mappings will be constructed by applying (sequences of) nonlinear transformations to known contraction mappings. We recall that these transformations are also used in turning a linear operator into nonlinear one [1][2][3][4][5]. Thanks to these sequences of non-affine contraction mappings, it is possible to obtain (a sequence of) new iterated function systems.…”

Section: Introductionmentioning

confidence: 99%

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Approximation to the classical fractals by using non-affine contraction mappings

Aslan

2022

Port. Math.

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In the literature, there are various methods to obtain the fractal sets such as escape time algorithm, L-systems and iterated function system (IFS), etc. In this study, we aim to approximate to the classical fractals by using non-affine contraction mappings. In order to get these non-affine mappings, we utilize from the sequences of suitable Lipschitz continuous functions. Then, we obtain some approximations to the fractals which can be constructed as the attractor of an IFS. Finally, we give some illustrations for some specific cases.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximation to the classical fractals by using non-affine contraction mappings

Aslan

2022

Port. Math.

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“…In this section, we examine the order of convergence by means of g-modulus of continuity. To this end, as in [5,6,7,8,9,10,34], we take into account the following definitions. Let (u w ) and (v w ) be a sequence of positive real numbers.…”

mentioning

confidence: 99%

Approximation by pseudo-linear discrete operators

Aslan¹,

Gökçer²

2023

MFC

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<p style='text-indent:20px;'>In this note, we construct a pseudo-linear kind discrete operator based on the continuous and nondecreasing generator function. Then, we obtain an approximation to uniformly continuous functions through this new operator. Furthermore, we calculate the error estimation of this approach with a modulus of continuity based on a generator function. The obtained results are supported by visualizing with an explicit example. Finally, we investigate the relation between discrete operators and generalized sampling series.</p>

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