Iterative Approximation of Fixed Points for Asymptotically Strict Pseudocontractive Type Mappings in the Intermediate Sense

Abstract

We introduced the concept of an asymptotically $\kappa$-strict pseudocontractive type mapping in the intermediate sense which is not necessarily Lipschitzian. We proved that the modified Mann iteration process: $x_{n+1} = (1-\alpha_n) x_n + \alpha_n T^n x_n$, $\forall n \geq 1$ where $\{\alpha_n\}$ is a sequence in $(0,1)$ with $\delta \leq \alpha_n \leq 1 - \kappa - \delta$ for $\delta \in (0,1)$ converges weakly to a fixed point of an asymptotically $\kappa$-strict pseudocontractive type mapping $T$ in the intermediate sense. Furthermore, a CQ method which generates a strongly convergent sequence for this class of mappings is proposed and strong convergence result for this CQ method is established.