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Title: Fractals via Jungck type iterative schemes with S-Convexity
Authors: Tanveer, Muhammad
Keywords: Physical Sciences
Issue Date: 2020
Publisher: The University of Lahore, Lahore.
Abstract: Today fractals play an important role in many fields, e.g., image compression or encryption, biology, physics etc. One of the earliest studied fractal types was the Mandelbrot and Julia sets. These fractals have been generalized in many different ways. One of such generalizations is the use of various iteration processes from fixed point theory. In this thesis, we study the use of Jungck type iterative schemes (i.e. Jungck-Mann, Jungck-Ishikawa, Jungck-S, Jungck-Noor, Jungck-CR and Jungck-SP iterative schemes respectively) extended further by the use of s-convex combination. The Jungck type iterative schemes with s-convexity are implicit iterations in one, two and three steps. We define the orbits of Jungck-Mann, Jungck-Ishikawa, JungckS, Jungck-Noor, Jungck-CR and Jungck-SP iterative schemes with s-convexity and prove new escape criterion for the generation of fractals (i.e. Julia sets, Mandelbrot sets, Multi-corn sets, Biomorphs, Multi-brot and Multi-cardioid sets respectively) via the proposed iterative schemes. We develop the algorithms for proposed iterative schemes with s-convexity. We present the simple Julia set (i.e. boundary of filled Julia set) in the orbits of Jungck type iterative schemes, we show internal structure of Julia set and establish the correspondence between Julia points via dark blue lines in graphs. We generate Mandelbrot sets and Multi-corn sets in the orbits of Jungck type iterative schemes with s-convexity. Also we visualize the biological resembled images in the form of biomorphs. In biomorph generation algorithm, we did not fixed the threshold radius of proposed orbits as fixed in literature earlier. Moreover, we generate the fractals of rational complex functions in established orbits. We present some graphical experiments obtained by the use of escape time algorithms and the derived criterion. The experiments show how the image change with the change of input parameters and also calculate the image generation time.
Gov't Doc #: 20203
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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