Iteration Approximation for Fixed Point of Nonlinear $\Phi$-Pseudocontractive Mappings in Banach Spaces

Abstract:

      This paper deals with the iteration approximation problem of fixed point for the nonlinear quasi-$\Phi$-pseudocontractive mappings and $\Phi$-pseudocontractive mappings. The results presented in this paper show that the quasi-$\Phi$-pseudocontractive mapping and $\Phi$-pseudocontractive mapping $T$~($T$ may not be continuous) of the Ishikawa and Mann iterative sequences with errors converges strongly to the unique fixed point of $T$ in an arbitrary real Banach space $E$. Our results improve and extend some recent results, and improve the methods of proof.