Kantorovich-Bernstein α-fractal function in 𝓛P spaces

Chand, A. K. B.; Jha, Sangita; Navascués, M. A.

doi:10.2989/16073606.2019.1572664

Cited by 10 publications

(3 citation statements)

References 16 publications

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“…Corollary 3.15. If we consider the Bernstein polynomial as the base function, then for a Lipschitz f , we obtain a sequence of Bernstein α-fractal functions (see [8,28] for details). For each n ∈ N, let G be the graph of the Bernstein α-fractal function.…”

Section: Oscillation Spacesmentioning

confidence: 99%

Dimensional analysis of fractal interpolation functions

Verma¹,

Jha²

2020

Preprint

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Section: Oscillation Spacesmentioning

confidence: 99%

Dimensional analysis of fractal interpolation functions

Verma¹,

Jha²

2020

Preprint

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“…Initially, Barnsley worked on a ne fractal interpolation functions using a ne transformations. Later on, more general transformations apart from a ne ones have been explored to construct quadratic fractal interpolation function, α-fractal interpolation function, hidden variable fractal interpolation function, and so on, for more details see [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Beyond the approximation theory, fractals are also compiled with various elds such as graph theory [16,17] and fractional calculus [18,19].…”

Section: Introductionmentioning

confidence: 99%

On Approximation Properties of Fractional Integral for A-Fractal Function

Priyanka

Valarmathi

Bingi

et al. 2022

Mathematical Problems in Engineering

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In this paper, the Riemann–Liouville fractional integral of an A-fractal function is explored by taking its vertical scaling factors in the block matrix as continuous functions from 0,1 to ℝ . As the scaling factors play a significant role in the generation of fractal functions, the necessary condition for the scaling factors in the block matrix is outlined for the newly obtained function. The resultant function of the fractional integral is demonstrated as an A-fractal function if the scaling factors obey the necessary conditions. Furthermore, this article proposes a fractional operator which defines the Riemann–Liouville fractional integral of an A-fractal function for each continuous function on C I , ℝ 2 , where C I , ℝ 2 is the space of all continuous functions from closed interval I ⊂ ℝ to ℝ 2 . In addition, the approximation properties such as linearity, boundedness, and semigroup property of the proposed fractional operator are investigated.

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“…The existence of invariant sets of IFS proceeds from the Banach fixed point theorem in a complete metric space. IFS portrays a decisive role in the development and applications of fractal interpolation functions in approximation theory and geometric modelling, see for instance [4][5][6]9,13,[17][18][19]25,26].…”

Section: Introductionmentioning

confidence: 99%

Cyclic Meir-Keeler Contraction and Its Fractals

Pasupathi

Chand

Navascués

2021

Numerical Functional Analysis and Optimization

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In present times, there has been a substantial endeavor to generalize the classical notion of iterated function system (IFS). We introduce a new type of non-linear contraction namely cyclic Meir-Keeler contraction, which is more generic than the famous Banach contraction. We show the perseverance and uniqueness of the fixed point for the cyclic Meir-Keeler contraction. Using this result, we propose the cyclic Meir-Keeler IFS in the literature for construction of fractals. Furthermore, we extend the theory of countable IFS and generalized IFS by using these cyclic Meir-Keeler contraction maps.

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Kantorovich-Bernstein α-fractal function in 𝓛^P spaces

Cited by 10 publications

References 16 publications

Dimensional analysis of fractal interpolation functions

Dimensional analysis of fractal interpolation functions

On Approximation Properties of Fractional Integral for A-Fractal Function

Cyclic Meir-Keeler Contraction and Its Fractals

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