Non Linear Dynamics of Ishikawa Iteration

Rana, Rajeshri; Chauhan, Yashwant Singh; Negi, Ashish

doi:10.5120/1320-1674

Cited by 20 publications

(15 citation statements)

References 14 publications

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“…Definition 3.1. ( [15,16]) The sequences {x n } and {y n } constructed above is called S-scheme sequences of iterations or relative superior sequences of iterates. We denote it by RSO(x 0 , s n , s ′ n , t).…”

Section: S-iteration Scheme For Relative Superior Mandelbrot Setsmentioning

confidence: 99%

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Fractals through modified iteration scheme

Kang

Rafiq

Latif

et al. 2016

Filomat

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In this paper we study the geometry of relative superior Mandelbrot sets through S-iteration scheme. Our results are quit significant from other Mandelbrot sets existing in the literature. Besides this, we also observe that S-iteration scheme converges faster than Ishikawa iteration scheme. We believe that the results of this paper can be inspired those who are interested in creating automatically aesthetic patterns.

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Section: S-iteration Scheme For Relative Superior Mandelbrot Setsmentioning

confidence: 99%

“…Rani and Kumar [16] introduced the superior Mandelbrot sets using Mann iteration scheme. Rana et al [15] introduced relative superior Mandelbrot sets using Ishikawa iteration seheme. They also explored relative superior Mandelbrot sets of quadraties, cubic and other complex values polynomials and discuss some related properties.…”

Section: Introductionmentioning

confidence: 99%

Fractals through modified iteration scheme

Kang

Rafiq

Latif

et al. 2016

Filomat

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“…where 0 ≤ n ≥ 1 and 0 ≤ n ≥ 1 and n & n both convergent to non zero number. [4] The sequences {x n } and {y n } constructed above is called Ishikawa sequences of iteration or relative superior sequences of iterate. We denote it by RSO(x 0 , n , n, t).Notice that RSO (x 0 , n , n, t) with n = 1 is RSO(x 0 , n , t) i.e.…”

Section: Preliminaries 1 Ishikawa Iterationmentioning

confidence: 99%

New Julia and Mandelbrot Sets for Jungck Ishikawa Iterates

Joshi¹,

Chauhan²,

Negi³

2014

IJCTT

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The generation of fractals and study of the dynamics of polynomials is one of the emerging and interesting field of research nowadays. We introduce in this paper the dynamics of polynomials z n -z + c = 0 for n  2 and applied Jungck Ishikawa Iteration to generate new Relative Superior Mandelbrot sets and Relative Superior Julia sets. In order to solve this function by Jungck -type iterative schemes, we write it in the form of Sz = Tz, where the function T, S are defined as Tz = z n + c and Sz = z.Only mathematical explanations are derived by applying Jungck Ishikawa Iteration for polynomials in the literature but in this paper we have generated Relative Mandelbrot sets and Relative Julia sets.

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“…So, |z | ≥ c |, and |z |>2/s as well as |z |>2/ s ' shows the escape criteria for quadratics. [14] Suppose that |z | >max {|b | , (a+ 2 /s) ½ , (a+ 2 /s ') ½ }, then |z n |→∞ as n →∞ .This gives the escape criteria for cubic polynomials.…”

Section: Generating the Fractalsmentioning

confidence: 99%

Complex Dynamics of Jungck Ishikawa Iterates for Hyperbolic Cosine Function

Pant¹,

Chauhan²,

Dimri³

2014

IJCA

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The dynamics of transcendental function is one of emerging and interesting field of research nowadays. We introduce in this paper the complex dynamics of hyperbolic cosine function of the type {cosh (z n ) + z + c = 0} and applied Jungck Ishikawa iteration to generate new Relative Superior Mandelbrot set and Relative Superior Julia set. In order to solve this function by Jungck -type iterative schemes, we write it in the form of Sz = Tz, where the function T, S are defined as Tz = cosh( z n ) +c and Sz = -z. Only mathematical explanations are derived by applying Jungck Ishikawa Iteration for transcendental function in the literature but in this paper we have generated relative Mandelbrot sets and Relative Julia sets.

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Non Linear Dynamics of Ishikawa Iteration

Cited by 20 publications

References 14 publications

Fractals through modified iteration scheme

Fractals through modified iteration scheme

New Julia and Mandelbrot Sets for Jungck Ishikawa Iterates

Complex Dynamics of Jungck Ishikawa Iterates for Hyperbolic Cosine Function

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