Asymptotically orientation-preserving mappings in Banach 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...

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

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.

On Asymptotically Symmetric Banach Spaces

A Banach space X is asymptotically symmetric (a.s.) if for some C <∞, for all m ∈ N, for all bounded sequences (xj)j=1 ⊆ X, 1 ≤ i ≤ m, for all permutations σ of {1, . . . ,m} and all ultrafilters U1, . . . ,Um on N, lim n1,U1 . . . lim nm,Um ∥∥∥∥ m ∑ i=1 xini ∥∥∥∥ ≤ C lim nσ(1),Uσ(1) . . . lim nσ(m),Uσ(m) ∥∥∥∥ m ∑

Convergence results‎: ‎A new type iteration scheme for two asymptotically nonexpansive mappings in uniformly convex Banach spaces

‎In this article‎, ‎we introduce a new type iterative scheme for‎ ‎approximating common fixed points of two asymptotically‎ ‎nonexpansive mappings is defined‎, ‎and weak and strong convergence‎ ‎theorem are proved for the new iterative scheme in a uniformly‎ ‎convex Banach space‎. ‎The results obtained in this article‎ ‎represent an extension as well as refinement of previous known‎ ‎resu...