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

Hafiz Fukhar-ud-din | Zendy; Vasile Berinde | Zendy

Open Access

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

Author(s) -

Hafiz Fukhar-ud-din,

Vasile Berinde

Publication year - 2016

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1601223f

Subject(s) - mathematics , rate of convergence , convergence (economics) , iterative method , metric (unit) , metric space , regular polygon , class (philosophy) , convex metric space , type (biology) , space (punctuation) , pure mathematics , mathematical optimization , computer science , geometry , artificial intelligence , computer network , channel (broadcasting) , operations management , ecology , economics , biology , economic growth , operating system

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

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