Fractal Generation via CR Iteration Scheme With S-Convexity

Fixed point results for fractal generation in Noor orbit and s-convexity

In this note, we give fixed point results in fractal generation (Julia sets and Mandelbrot sets) by using Noor iteration scheme with s-convexity. Researchers have already presented fixed point results in Mann and Ishikawa orbits that are examples of one-step and two-step feedback processes respectively. In this paper we present fixed point results in Noor orbit, which is a three-step iterative ...

Strong Convergence for Hybrid S-Iteration Scheme

Polynomial Approximation, Local Polynomial Convexity, and Degenerate Cr Singularities

We begin with the following question: given a closed disc D b C and a complexvalued function F ∈ C(D), is the uniform algebra on D generated by z and F equal to C(D) ? When F ∈ C1(D), this question is complicated by the presence of points in the surface S := graphD(F ) that have complex tangents. Such points are called CR singularities. Let p ∈ S be a CR singularity at which the order of contac...

Adaptive Segmentation with Optimal Window Length Scheme using Fractal Dimension and Wavelet Transform

In many signal processing applications, such as EEG analysis, the non-stationary signal is often required to be segmented into small epochs. This is accomplished by drawing the boundaries of signal at time instances where its statistical characteristics, such as amplitude and/or frequency, change. In the proposed method, the original signal is initially decomposed into signals with different fr...

Polynomial Approximation, Local Polynomial Convexity, and Degenerate Cr Singularities

We begin with the following question: given a closed disc D ⋐ C and a complex-valued function F ∈ C(D), is the uniform algebra on D generated by z and F equal to C(D) ? When F ∈ C 1 (D), this question is complicated by the presence of points in the surface S := graph D (F) that have complex tangents. Such points are called CR singularities. Let p ∈ S be a CR singularity at which the order of co...