UGC Approved Journal no 63975

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Published in:

Volume 6 Issue 6
June-2019
eISSN: 2349-5162

UGC and ISSN approved 7.95 impact factor UGC Approved Journal no 63975

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Published Paper ID:
JETIR1908B33


Registration ID:
227937

Page Number

230-239

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Title

APPLICATIONS OF PICARD ISHIKAWA TYPE FIXED POINT ITERATION FOR CONSTRUCTION OF FRACTALS

Abstract

Complex Polynomials P_C(x) = x^n + m x + r where m, r ∈C appeared in various engineering problems such as digital image processing. These Polynomials are very useful for the determination of pole-zero plots for signals and to study the structure and solutions of linear time invariant space models [15], hence the study of behaviour of these polynomials and their Julia and Mandelbrot sets is interested area of research. Some researchers introduced Julia and Mandelbrot sets in implicit Jungck Mann and Jungck Ishikawa orbits and they worked on this implicit iteration process to construct graphical structure of these complex polynomials, for this they divide the polynomial into two parts as P_1(x) = x^n + r and P_2(x) = m x then the Jungck iteration process and its variants are useful for determination of the common fixed points of these two maps. So we get an escape criterion and generate fractals for polynomials of mentioned form with the help of iteration processes. In present paper we apply Picard Ishikawa type fixed point iteration method for the construction of fractals such as Mandelbrot set and Julia set for some complex polynomials and obtain graphical output of these sets, we establishes some results for the construction of Mandelbrot set and Julia set with time escape. Also we compare some attributes or parameters with the help of advanced software’s like MATLAB. In particularly the graphical behaviour of the complex polynomial of the form P_C(x) = x^n + m x + r where m, r ∈C and n ≥ 2 by using Picard Ishikawa type fixed point iteration process for the construction of fractals.

Key Words

Fixed point, iteration, fractal geometry, MATLAB.

Cite This Article

"APPLICATIONS OF PICARD ISHIKAWA TYPE FIXED POINT ITERATION FOR CONSTRUCTION OF FRACTALS ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 6, page no.230-239, June-2019, Available :http://www.jetir.org/papers/JETIR1908B33.pdf

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2349-5162 | Impact Factor 7.95 Calculate by Google Scholar

An International Scholarly Open Access Journal, Peer-Reviewed, Refereed Journal Impact Factor 7.95 Calculate by Google Scholar and Semantic Scholar | AI-Powered Research Tool, Multidisciplinary, Monthly, Multilanguage Journal Indexing in All Major Database & Metadata, Citation Generator

Cite This Article

"APPLICATIONS OF PICARD ISHIKAWA TYPE FIXED POINT ITERATION FOR CONSTRUCTION OF FRACTALS ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 6, page no. pp230-239, June-2019, Available at : http://www.jetir.org/papers/JETIR1908B33.pdf

Publication Details

Published Paper ID: JETIR1908B33
Registration ID: 227937
Published In: Volume 6 | Issue 6 | Year June-2019
DOI (Digital Object Identifier):
Page No: 230-239
Country: -, -, - .
Area: Engineering
ISSN Number: 2349-5162


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