On iterative solution of nonlinear functional equations in a metric space
Given that A and P as nonlinear onto and into self-mappings of a complete metric space R, we offer here a constructive proof of the existence of the unique solution of the operator equation Au=Pu, where u∈R, by considering the iterative sequence Aun+1=Pun (u0 prechosen, n=0,1,2,…). We use Kannan...
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| Format: | Article |
| Language: | English |
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Wiley
1983-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171283000149 |
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| _version_ | 1832562861854949376 |
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| author | Rabindranath Sen Sulekha Mukherjee |
| author_facet | Rabindranath Sen Sulekha Mukherjee |
| author_sort | Rabindranath Sen |
| collection | DOAJ |
| description | Given that A and P as nonlinear onto and into self-mappings of a complete metric space R, we offer here a constructive proof of the existence of the unique solution of the operator equation Au=Pu, where u∈R, by considering the iterative sequence Aun+1=Pun (u0 prechosen, n=0,1,2,…). We use Kannan's criterion [1] for the existence of a unique fixed point of an operator instead of the contraction mapping principle as employed in [2]. Operator equations of the form Anu=Pmu, where u∈R, n and m positive integers, are also treated. |
| format | Article |
| id | doaj-art-269a719411904cd9bb1ed174645bc3c9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1983-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-269a719411904cd9bb1ed174645bc3c92025-02-03T01:21:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251983-01-016116117010.1155/S0161171283000149On iterative solution of nonlinear functional equations in a metric spaceRabindranath Sen0Sulekha Mukherjee1Department of Applied Mathematics, University College of Science, 92 Acharya Prafulla Chandra Road, Calcutta 700009, IndiaDepartment of Mathematics, University of Kalyani, Kalyani, Dt. Nadia, West Bengal, IndiaGiven that A and P as nonlinear onto and into self-mappings of a complete metric space R, we offer here a constructive proof of the existence of the unique solution of the operator equation Au=Pu, where u∈R, by considering the iterative sequence Aun+1=Pun (u0 prechosen, n=0,1,2,…). We use Kannan's criterion [1] for the existence of a unique fixed point of an operator instead of the contraction mapping principle as employed in [2]. Operator equations of the form Anu=Pmu, where u∈R, n and m positive integers, are also treated.http://dx.doi.org/10.1155/S0161171283000149Kannan's fixed point theoremnonlinear integral equation. |
| spellingShingle | Rabindranath Sen Sulekha Mukherjee On iterative solution of nonlinear functional equations in a metric space International Journal of Mathematics and Mathematical Sciences Kannan's fixed point theorem nonlinear integral equation. |
| title | On iterative solution of nonlinear functional equations in a metric space |
| title_full | On iterative solution of nonlinear functional equations in a metric space |
| title_fullStr | On iterative solution of nonlinear functional equations in a metric space |
| title_full_unstemmed | On iterative solution of nonlinear functional equations in a metric space |
| title_short | On iterative solution of nonlinear functional equations in a metric space |
| title_sort | on iterative solution of nonlinear functional equations in a metric space |
| topic | Kannan's fixed point theorem nonlinear integral equation. |
| url | http://dx.doi.org/10.1155/S0161171283000149 |
| work_keys_str_mv | AT rabindranathsen oniterativesolutionofnonlinearfunctionalequationsinametricspace AT sulekhamukherjee oniterativesolutionofnonlinearfunctionalequationsinametricspace |