The general results on convergence of the Ishikawa iteration procedures with errors for Lipschitzian φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type is established in arbit...The general results on convergence of the Ishikawa iteration procedures with errors for Lipschitzian φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type is established in arbitrary Banach spaces. As the direct applications, some stability results of the Ishikawa iteration methods for φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type are also given. Our results in this paper improve and extend the recent results due to Osilike and other authors.展开更多
<正>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 ...<正>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 in[0,1].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.展开更多
基金the National Natural Science Foundation of China ( Grant No.1 9971 0 1 3)
文摘The general results on convergence of the Ishikawa iteration procedures with errors for Lipschitzian φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type is established in arbitrary Banach spaces. As the direct applications, some stability results of the Ishikawa iteration methods for φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type are also given. Our results in this paper improve and extend the recent results due to Osilike and other authors.
基金This work was supported partially by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions by Ministry of Educationthe Department Fund of Science and Technology in Shanghai Higher Education Institutionsthe Special Funds for Major Specialities by the Shanghai Education Committee.
文摘<正>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 in[0,1].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.
