Asymptotically Nonexpansive Mappings in Modular Function Spaces

Convergence Theorems for Asymptotically Nonexpansive Mappings in Banach Spaces

Let E be a uniformly convex Banach space, and let K be a nonempty convex closed subset which is also a nonexpansive retract of E. Let T : K → E be an asymptotically nonexpansive mapping with {kn} ⊂ [1,∞) such that P∞ n=1(kn − 1) < ∞ and let F (T ) be nonempty, where F (T ) denotes the fixed points set of T . Let {αn}, {βn}, {γn}, {αn}, {β′ n}, {γ′ n}, {α′′ n}, {β′′ n} and {γ′′ n} be real sequen...

Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces

This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnosel’skiı̆–Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the fixed po...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Fixed Points of Asymptotic Pointwise Nonexpansive Mappings in Modular Spaces

The theory of modular spaces was initiated by Nakano 1 in 1950 in connection with the theory of order spaces and redefined and generalized by Musielak and Orlicz 2 in 1959. These spaces were developed following the successful theory of Orlicz spaces, which replaces the particular, integral form of the nonlinear functional, which controls the growth of members of the space, by an abstractly give...

Convergence theorems of implicit iterates with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces

In this paper, we prove that an implicit iterative process with er-rors converges strongly to a common xed point for a nite family of generalizedasymptotically quasi-nonexpansive mappings on unbounded sets in a uniformlyconvex Banach space. Our results unify, improve and generalize the correspond-ing results of Ud-din and Khan [4], Sun [21], Wittman [23], Xu and Ori [26] andmany others.