Iterative approximation problem of fixed points for uniformly \(L\)-Lipschitz and asymptotically pseudocontractive mappings. (Chinese. English summary) Zbl 1230.47099
Summary: The purpose of this paper is to investigate the strong convergence of the modified Ishikawa and Mann iterative processes with errors for approximating fixed points of uniformly \(L\)-Lipschitzian and asymptotically pseudocontractive mappings in an arbitrary real Banach space. By removing the restriction
\[
\sum\limits^\infty_{n=0}\alpha^2_n<\infty,\;\sum\limits^\infty_{n=0}\gamma_n<\infty,\;\sum\limits^\infty_{n=0}\alpha_n(\beta_n+\delta_n)<\infty, \;\sum\limits^\infty_{n=0}\alpha_n(k_n-1)<\infty,
\]
it is proven that the relevant results remain true. The results presented in this paper improve and extend some recent existing results.
MSC:
47J25 | Iterative procedures involving nonlinear operators |
47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
47H10 | Fixed-point theorems |