scholarly journals New escape conditions with general complex polynomial for fractals via new fixed point iteration

2021 ◽  
Vol 6 (6) ◽  
pp. 5563-5580
Author(s):  
Muhammad Tanveer ◽  
◽  
Imran Ahmed ◽  
Ali Raza ◽  
Sumaira Nawaz ◽  
...  
Keyword(s):  
Fixed Point ◽  
Complex Polynomial ◽  
Fixed Point Iteration ◽  
General Complex

scholarly journals Fixed point results of an implicit iterative scheme for fractal generations

2021 ◽  
Vol 6 (12) ◽  
pp. 13170-13186
Author(s):  
Haixia Zhang ◽  
◽  
Muhammad Tanveer ◽  
Yi-Xia Li ◽  
Qingxiu Peng ◽  
...  
Keyword(s):  
Fixed Point ◽  
Iterative Scheme ◽  
Mandelbrot Set ◽  
Complex Polynomial ◽  
Ishikawa Iteration ◽  
General Complex ◽  
Implicit Iterative Scheme ◽  
Implicit Iteration

<abstract><p>In this paper, we derive the escape criteria for general complex polynomial $ f(x) = \sum_{i = 0}^{p}a_{i}x^{i} $ with $ p\geq2 $, where $ a_{i} \in \mathbb{C} $ for $ i = 0, 1, 2, \dots, p $ to generate the fractals. Moreover, we study the orbit of an implicit iteration (i.e., Jungck-Ishikawa iteration with $ s $-convexity) and develop algorithms for Mandelbrot set and Multi-corn or Multi-edge set. Moreover, we draw some complex graphs and observe how the graph of Mandelbrot set and Multi-corn or Multi-edge set vary with the variation of $ a_{i} $'s.</p></abstract>

scholarly journals Differentiable Forward and Backward Fixed-Point Iteration Layers

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 18383-18392
Author(s):  
Younghan Jeon ◽  
Minsik Lee ◽  
Jin Young Choi
Keyword(s):  
Fixed Point ◽  
Fixed Point Iteration

scholarly journals On the Equivalence of Implicit Kirk-Type Fixed Point Iteration Schemes for a General Class of Maps

2019 ◽  
Vol 07 (01) ◽  
pp. 123-137
Author(s):  
Alfred Olufemi Bosede ◽  
Hudson Akewe ◽  
Omolara Fatimah Bakre ◽  
Ashiribo Senapon Wusu
Keyword(s):  
Fixed Point ◽  
General Class ◽  
Fixed Point Iteration

scholarly journals Application of the Robust Fixed Point Iteration Method in Control of the Level of Twin Tanks Liquid

Computation ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 96
Author(s):  
Hamza Khan ◽  
Hazem Issa ◽  
József K. Tar
Keyword(s):  
Numerical Simulation ◽  
Fixed Point ◽  
Nonlinear Systems ◽  
Flow Rate ◽  
Fluid Level ◽  
Process Industries ◽  
Fixed Point Iteration ◽  
Precise Control ◽  
Strongly Nonlinear ◽  
Simulation Results

Precise control of the flow rate of fluids stored in multiple tank systems is an important task in process industries. On this reason coupled tanks are considered popular paradigms in studies because they form strongly nonlinear systems that challenges the controller designers to develop various approaches. In this paper the application of a novel, Fixed Point Iteration (FPI)-based technique is reported to control the fluid level in a “lower tank” that is fed by the egress of an “upper” one. The control signal is the ingress rate at the upper tank. Numerical simulation results obtained by the use of simple sequential Julia code with Euler integration are presented to illustrate the efficiency of this approach.

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