On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces
The purpose of this paper is to consider a new implicit iteration and study its strong convergence, stability, and data dependence. It is proved through numerical examples that newly introduced iteration has better convergence rate than well known implicit Mann iteration as well as implicit Ishikawa...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/905834 |
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| _version_ | 1832545788465512448 |
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| author | Renu Chugh Preety Malik Vivek Kumar |
| author_facet | Renu Chugh Preety Malik Vivek Kumar |
| author_sort | Renu Chugh |
| collection | DOAJ |
| description | The purpose of this paper is to consider a new implicit iteration and study its strong convergence, stability, and data dependence. It is proved through numerical examples that newly introduced iteration has better convergence rate than well known implicit Mann iteration as well as implicit Ishikawa iteration and implicit iterations converge faster as compared to corresponding explicit iterations. Applications of implicit iterations to RNN (Recurrent Neural Networks) analysis are also presented. |
| format | Article |
| id | doaj-art-6ce47b7d42624405babfae8363dd6a0b |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-6ce47b7d42624405babfae8363dd6a0b2025-02-03T07:24:49ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/905834905834On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric SpacesRenu Chugh0Preety Malik1Vivek Kumar2Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, IndiaDepartment of Mathematics, Maharshi Dayanand University, Rohtak 124001, IndiaDepartment of Mathematics, KLP College, Rewari 123401, IndiaThe purpose of this paper is to consider a new implicit iteration and study its strong convergence, stability, and data dependence. It is proved through numerical examples that newly introduced iteration has better convergence rate than well known implicit Mann iteration as well as implicit Ishikawa iteration and implicit iterations converge faster as compared to corresponding explicit iterations. Applications of implicit iterations to RNN (Recurrent Neural Networks) analysis are also presented.http://dx.doi.org/10.1155/2015/905834 |
| spellingShingle | Renu Chugh Preety Malik Vivek Kumar On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces Journal of Function Spaces |
| title | On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces |
| title_full | On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces |
| title_fullStr | On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces |
| title_full_unstemmed | On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces |
| title_short | On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces |
| title_sort | on a new faster implicit fixed point iterative scheme in convex metric spaces |
| url | http://dx.doi.org/10.1155/2015/905834 |
| work_keys_str_mv | AT renuchugh onanewfasterimplicitfixedpointiterativeschemeinconvexmetricspaces AT preetymalik onanewfasterimplicitfixedpointiterativeschemeinconvexmetricspaces AT vivekkumar onanewfasterimplicitfixedpointiterativeschemeinconvexmetricspaces |