Fractals and Chaos in Noor Orbit

In this book, the author develops the four-step feedback scheme and introduces the fixed-point results using Noor iterative procedure. The findings connect many area of mathematics and computer science, including fractal geometry, chaos theory, number theory, spectral geometry, dynamical systems, complex analysis, functional analysis, nonlinear programming, graphics, and computer programming. New Julia sets, Mandelbrot sets, anti-Julia sets, and Cantor sets have been defined, generated, and analyzed using Noor iterative procedure. Cantor set has enjoyed its classic properties in fractal theory and the study of Cantor one-fifth set as an example of fractal string has been analyzed. After a formal study on Julia and Mandelbrot sets, the concept of stability of functional equations is also explained in brief. Moreover, our findings will be of great importance in improving the various applications in science and engineering such as cryptography, secure communication system, transportation problems, etc.