Iterative methods for the class of quasi-contractive type operators and comparsion of their rate of convergence in convex metric spaces

Abstract

We introduce modified Noor iterativemethod in a convex metric space and apply it to approximate fixed points ofquasi-contractive operators introduced by Berinde \cite{Berinde(2005-2)}.Our results generalize and improve upon, among others, the correspondingresults of Berinde \cite{Berinde(2005-2)}, Bosede \cite{Bosede} andPhuengrattana and Suantai \cite{Phu- Suantai}. We also compare the rate ofconvergence of proposed iterative method to the iterative methods due toNoor \cite{XuNoor}, Ishikawa \cite{Ishikawa} and Mann \cite{Mann}. It hasbeen observed that the proposed method is faster than the other threemethods. Incidently the results obtained herein provide analogues of thecorresponding results of normed spaces and holds in $CAT(0)$ spaces,simultaneously.