Convergence theorems for a general class of nonexpansive mappings in Banach spaces

In this paper, we introduce a new iteration process for the approximation of fixed points. We show that our iteration process is faster than the existing iteration processes like the M-iteration process and the K-iteration process for contraction mappings. Also, we prove that the new iteration process is stable. Finally, we study the convergence of a new iterative scheme to a fixed point for the (\alpha,\beta) -Reich-Suzuki nonexpansive type mappings in Banach space.

Keywords:

Fixed point , convergence , Opial’s condition , generalized nonexpansive mappings