The aim of this paper is to establish some fixed point results in the generation of Julia and Mandelbrot sets by using Jungck Mann and Jungck Ishikawa iterations with s-convexity.
In this paper, we describe the new Husehölder's method free from second derivatives for solving nonlinear equations. The new Husehölder's method has convergence of order five and efficiency index 5 1 3 ≈ 1.70998, which converges faster than the Newton's method, the Halley's method and the Husehölder's method. The comparison table demonstrate the faster convergence of our method. Polynomiography via the new Husehölder's method is also presented.
We establish new fixed point results in the generation of fractals (Julia sets, Mandelbrot sets, and Tricorns and Multicorns for linear or nonlinear dynamics) by using Jungck Noor iteration withs-convexity.
In this paper, we present two new numerical algorithms for solving nonlinear equations based on Newton-Raphson method. New algorithms are constructed by using modified Adomian decomposition. The efficiency of new algorithms is shown by solving some numerical examples.
The aim of this paper is to present some artwork produced via polynomiography of a few complex polynomials and a few special polynomials arising in science as well as a few considered to arrive at beautiful but anticipated designs. In this paper an iterative method corresponding to Simpson's 1 3 rule is used instead of Newton's method. The word "polynomiography" coined by Kalantari for that visualization process. The images obtained are called polynomiographs. Polynomiographs have importance for both the art and science aspects. By using an iterative method corresponding to Simpson's 1 3 rule, we obtain quite new nicely looking polynomiographs that are different from Newton's method. Presented examples show that we obtain very interesting patterns for complex polynomial equations, permutation matrices, doubly stochastic matrices, Chebyshev polynomial, polynomial arising in physics and Alexander polynomial in knot theory. We believe that the results of this paper enrich the functionality of the existing polynomiography software. c 2016 All rights reserved.
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