| Approximation Solutions of Nonlinear Strongly Accretive Operator Equations by Ishikawa Iteration Procedure with Errors |
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| 作者姓名： | Luchuan Zeng |
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| 作者单位： | Luchuan Zeng Department of Mathematics，Shanghai Normal University，Shanghai 200234，China. |
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| 基金项目： | This work was supported partially by the Teaching and Research Award Fund for 0utstanding Young Teachers in Higher Education Institutions by Ministry of Education, the Department Fund of Science and Technology in Shanghai Higher Education Institutions, and the Special Funds for Major Specialities by the Shanghai Education Committee. |
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| 摘 要： | Let 1＜ρ≤2,E be a real ρ-uniformly smooth Banach space and T:E→E be a continuous and strongly accretive operator.The purpose of this paper is to investigate the problem of approximating solutions to the equation Tx=f by the Ishikawa iteration procedure with errors (?) where x_0 ∈ E,{u_n},{υ_n}are bounded sequences in E and{α_n},{b_n},{c_n},{a_n~'},{b_n~'},{c_n~'} are real sequences in0,1].Under the assumption of the condition 0＜α≤b_n c_n,An≥0, it is shown that the iterative sequence{x_n}converges strongly to the unique solution of the equation Tx=f.Furthermore,under no assumption of the condition(?)(b_n~' c_n~')=0,it is also shown that{x_n}converges strongly to the unique solution of Tx=f.
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| 关 键 词： | Strongly accretive operator equation Ishikawa iteration procedure with errors solution ρ-uniformly smooth Banach space |
| 收稿时间： | 2003-07-12 |
| 修稿时间： | 2004-05-25 |
Approximation Solutions of Nonlinear Strongly Accretive Operator Equations by Ishikawa Iteration Procedure with Errors |
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| Luchuan Zeng.Approximation Solutions of Nonlinear Strongly Accretive Operator Equations by Ishikawa Iteration Procedure with Errors[J].Numerical Mathematics A Journal of Chinese Universities English Series,2006,15(1):31-39. |
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| Authors: | Luchuan Zeng |
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| Abstract: | Let 1 ＜ p ≤ 2, E be a real p-uniformly smooth Banach space and T: E → E be a continuous and strongly accretive operator. The purpose of this paper is to investigate the problem of approximating solutions to the equation Tx = f by the Ishikawa iteration procedure with errors{xn+1 = anxn + bn(f - Tyn + yn) + cnun,yn = a'nxn + b'n(f - Txn + xn) + c'nvn,n≥0where x0 ∈ E, {un}, {vn} are bounded sequences in E and {an}, {bn}, {cn}, {a'n}, {b'n}, {c'n}are real sequences in 0, 1]. Under the assumption of the condition 0 ＜α≤ bn + cn,(A)n ≥ 0,it is shown that the iterative sequence {xn} converges strongly to the unique solution of the equation Tx = f. Furthermore, under no assumption of the condition lim n→∞(b'n + c'n) = 0, it is also shown that {xn} converges strongly to the unique solution of Tx = f. |
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| Keywords: | Strongly accretive operator equation Ishikawa iteration procedure with errors solution p-uniformly smooth Banach space |
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