On the Convergence of Iterative Processes for Generalized Strongly Asymptotically ϕ-Pseudocontractive Mappings in Banach Spaces

Throughout this paper, we assume that X is a uniformly convex Banach space and X∗ is the dual space of X. Let J denote the normalized duality mapping form X into 2 ∗ given by J x {f ∈ X∗ : 〈x, f〉 ‖x‖2 ‖f‖2} for all x ∈ X, where 〈·, ·〉 denotes the generalized duality pairing. It is well known that if X is uniformly smooth, then J is single valued and is norm to norm uniformly continuous on any bounded subset of X. In the sequel, we will denote the single valued duality mapping by j. In 1967, Browder 1 and Kato 2 , independently, introduced accretive operators see, for details, Chidume 3 . Their interest is connectedwith the existence of results in the theory of nonlinear equations of evolution in Banach spaces. In 1972, Goebel and Kirk 4 introduced the class of asymptotically nonexpansive mappings as follows.