Equivalence of certain iteration processes via averaged mappings

Rizwan Anjum; Safeer Hussain Khan

doi:10.1007/s41478-023-00679-z

Equivalence of certain iteration processes via averaged mappings

Rizwan Anjum
, Safeer Hussain Khan

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we show that Picard, Mann, Ishikawa and Picard-Mann hybrid iterative processes associated with average mapping converge strongly to the fixed point of the mapping satisfies enriched Zamfirescu condition and all these iterative processes are equivalent to each others. An application of the main results to variational inequality problem are also given.

Original language	English
Pages (from-to)	1181-1198
Number of pages	18
Journal	Journal of Analysis
Volume	32
Issue number	2
DOIs	https://doi.org/10.1007/s41478-023-00679-z
State	Published - Apr 1 2024

Keywords

47H10
54H25
Average mapping
Enriched Zamfirescu condition
Fixed point
Iterative process

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10.1007/s41478-023-00679-z

Cite this

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abstract = "In this paper, we show that Picard, Mann, Ishikawa and Picard-Mann hybrid iterative processes associated with average mapping converge strongly to the fixed point of the mapping satisfies enriched Zamfirescu condition and all these iterative processes are equivalent to each others. An application of the main results to variational inequality problem are also given.",

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AB - In this paper, we show that Picard, Mann, Ishikawa and Picard-Mann hybrid iterative processes associated with average mapping converge strongly to the fixed point of the mapping satisfies enriched Zamfirescu condition and all these iterative processes are equivalent to each others. An application of the main results to variational inequality problem are also given.

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KW - 54H25

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KW - Enriched Zamfirescu condition

KW - Fixed point

KW - Iterative process

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Equivalence of certain iteration processes via averaged mappings

Abstract

Keywords

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