On the JK Iterative Process in Banach Spaces | Zendy

Junaid Ahmad | Zendy; Hüseyin Işık | Zendy; Faeem Ali | Zendy; Kifayat Ullah | Zendy; Eskandar Ameer | Zendy; Muhammad Arshad | Zendy

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On the JK Iterative Process in Banach Spaces

Author(s) -

Junaid Ahmad,

Hüseyin Işık,

Faeem Ali,

Kifayat Ullah,

Eskandar Ameer,

Muhammad Arshad

Publication year - 2021

Publication title -

journal of function spaces

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.579

H-Index - 28

eISSN - 2314-8896

pISSN - 2314-8888

DOI - 10.1155/2021/2500421

Subject(s) - banach space , iterative and incremental development , convergence (economics) , fixed point , mathematics , iterative method , scheme (mathematics) , class (philosophy) , discrete mathematics , pure mathematics , mathematical optimization , computer science , mathematical analysis , software engineering , artificial intelligence , economics , economic growth

In the recent progress, different iterative procedures have been constructed in order to find the fixed point for a given self-map in an effective way. Among the other things, an effective iterative procedure called the JK iterative scheme was recently constructed and its strong and weak convergence was established for the class of Suzuki mappings in the setting of Banach spaces. The first purpose of this research is to obtain the strong and weak convergence of this scheme in the wider setting of generalized α -nonexpansive mappings. Secondly, by constructing an example of generalized α -nonexpansive maps which is not a Suzuki map, we show that the JK iterative scheme converges faster as compared the other iterative schemes. The presented results of this paper properly extend and improve the corresponding results of the literature.

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