Nonlinear ergodic theorems for asymptotically nonexpansive mappings in Banach spaces satisfying Opial's condition

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

a mean ergodic theorem for asymptotically quasi-nonexpansive affine mappings in banach spaces satisfying opial's condition

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&apos;s condition

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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.