New Escape Criteria for Complex Fractals Generation in Jungck-CR Orbit

Muhammad Tanveer (), Waqas Nazeer () and Krzysztof Gdawiec ()
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Muhammad Tanveer: University of Lahore
Waqas Nazeer: University of Education
Krzysztof Gdawiec: Universityof Silesia

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1285-1303

Abstract: Abstract In recent years, researchers have studied the use of different iteration processes from fixed point theory for the generation of complex fractals. Examples are the Mann, the Ishikawa, the Noor, the Jungck-Mann and the Jungck-Ishikawa iterations. In this paper, we present a generalisation of complex fractals, namely Mandelbrot, Julia and multicorn sets, using the Jungck-CR implicit iteration scheme. This type of iteration does not reduce to any of the other iterations previously used in the study of complex fractals; thus, this generalisation gives rise to new fractal forms. We prove a new escape criterion for a polynomial of the following form zm − az + c, where a, c ∈ ℂ, and present some graphical examples of the obtained complex fractals.

Keywords: Julia set; Mandelbrot set; Jungck-CR orbit; escape criteria; 37F45; 47H10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s13226-020-0466-9

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