Escape criteria for one parameter family of complex functions \(\mathbf{f}_{\mathbf{k}}\left( \mathbf{z}\right)\mathbf{=}\mathbf{\text{kcsc}}\left( \mathbf{z} \right)\) via non-standard iterations

Document Type : Research Paper


1 Department of Mathematics and Computer Applications College of Science, Al-Nahrain University, Iraq

2 Department of Mathematics, College of Science, Baghdad University, Iraq

3 Al Ain University, Abu Dhabi, UAE


In this research we stated and proved the some escape criteria theorems of the one parameter family of the transcendental meromorphic-functions \(F\mathbf{=}\left\{ f_{k}\left( z \right) = k\ csc\left( z \right):k\mathbb{\in C\ }\text{and}\text{\ z}\mathbb{\in C} \right\}\). Furthermore, we used non-standard iterations: Mann, Ishikawa and Noor iterations in the complex plane. This research can be considered as an extension of [1].