Positive Solutions and Mann Iterative Algorithms for a Second-Order Nonlinear Difference Equation
This paper deals with the second-order nonlinear neutral delay difference equation Δ(anh(xn-τ1n,xn-τ2n,…,xn-τmn)Δ(xn-qnxn-τ0))+f(n,xn-σ1n,xn-σ2n,…,xn-σkn)=bn, n≥n0. Using the Banach fixed point theorem, Mann iterative method with errors, and some new techniques, we prove the existence of uncountably...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/8317567 |
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| _version_ | 1850212523889917952 |
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| author | Zeqing Liu Xin Li Shin Min Kang Young Chel Kwun |
| author_facet | Zeqing Liu Xin Li Shin Min Kang Young Chel Kwun |
| author_sort | Zeqing Liu |
| collection | DOAJ |
| description | This paper deals with the second-order nonlinear neutral delay difference equation Δ(anh(xn-τ1n,xn-τ2n,…,xn-τmn)Δ(xn-qnxn-τ0))+f(n,xn-σ1n,xn-σ2n,…,xn-σkn)=bn, n≥n0. Using the Banach fixed point theorem, Mann iterative method with errors, and some new techniques, we prove the existence of uncountably many positive solutions and the convergence of the sequences generated by the Mann iterative method with errors relative to these solutions for the above equation. Six examples are included. Our results extend and improve essentially the known results in this field. |
| format | Article |
| id | doaj-art-8a457ea12d0b4fecb1fbf40d54052a5a |
| institution | OA Journals |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-8a457ea12d0b4fecb1fbf40d54052a5a2025-08-20T02:09:18ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/83175678317567Positive Solutions and Mann Iterative Algorithms for a Second-Order Nonlinear Difference EquationZeqing Liu0Xin Li1Shin Min Kang2Young Chel Kwun3Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, ChinaSuizhong No. 1 Senior High School, Huludao, Liaoning 125200, ChinaDepartment of Mathematics and RINS, Gyeongsang National University, Jinju 52828, Republic of KoreaDepartment of Mathematics, Dong-A University, Busan 49315, Republic of KoreaThis paper deals with the second-order nonlinear neutral delay difference equation Δ(anh(xn-τ1n,xn-τ2n,…,xn-τmn)Δ(xn-qnxn-τ0))+f(n,xn-σ1n,xn-σ2n,…,xn-σkn)=bn, n≥n0. Using the Banach fixed point theorem, Mann iterative method with errors, and some new techniques, we prove the existence of uncountably many positive solutions and the convergence of the sequences generated by the Mann iterative method with errors relative to these solutions for the above equation. Six examples are included. Our results extend and improve essentially the known results in this field.http://dx.doi.org/10.1155/2016/8317567 |
| spellingShingle | Zeqing Liu Xin Li Shin Min Kang Young Chel Kwun Positive Solutions and Mann Iterative Algorithms for a Second-Order Nonlinear Difference Equation Journal of Function Spaces |
| title | Positive Solutions and Mann Iterative Algorithms for a Second-Order Nonlinear Difference Equation |
| title_full | Positive Solutions and Mann Iterative Algorithms for a Second-Order Nonlinear Difference Equation |
| title_fullStr | Positive Solutions and Mann Iterative Algorithms for a Second-Order Nonlinear Difference Equation |
| title_full_unstemmed | Positive Solutions and Mann Iterative Algorithms for a Second-Order Nonlinear Difference Equation |
| title_short | Positive Solutions and Mann Iterative Algorithms for a Second-Order Nonlinear Difference Equation |
| title_sort | positive solutions and mann iterative algorithms for a second order nonlinear difference equation |
| url | http://dx.doi.org/10.1155/2016/8317567 |
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