A New Three-Step Mixed-Type Implicit Iterative Scheme with Errors for Common Fixed Points of Nonexpansive and Uniformly $L$--Lipschitzian Asymptotically Generalized $Phi$-Hemicontractive Mappings

In this paper, we introduce a three-step implicit iteration scheme with errors for finite families of nonexpansive and uniformly $L$-Lipschitzian asymptotically generalized $Phi$-hemicontractive mappings in real Banach spaces. Our new implicit iterative scheme properly includes several well known iterative schemes in the literature as its special cases. The results presented in this paper extend, generalize and improve well known results in the existing literature.