In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of W -mappings of a countable family of ...

We introduce the notion of asymptotically almost nonexpansive curves which include almost-orbits of commutative semigroups of asymptotically nonexpansive type mappings and study the asymptotic behavior and prove nonlinear ergodic theorems for such curves. As applications of our main theorems, we obtain the results on the asymptotic behavior and ergodicity for a commutative semigroup of non-Lips...

In this paper, we first prove the weak convergence for the Moudafi’s iterative scheme of two quasi-nonexpansive mappings. Then we prove the weak convergence for the Moudafi’s iterative scheme of quasi-nonexpansive mapping and nonexpansive mapping. Finally, we prove the strong convergence for the Moudafi’s iterative scheme of two quasi-nonexpansive mappings. Our results generalize the recent res...

Tae-Hwa Kim and Hong-Kun Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis 64(2006)1140-1152 ] proved the strong convergence theorems of modified Mann iterations for asymptotically nonexpansive mappings and semigroups on bounded subset C of a Hilbert space by the CQ iteration method. The purpose of this paper is to mod...

and Applied Analysis 3 Lemma 2.2 cf., 4 . Let D be a nonempty subset of a reflexive, strictly convex, and smooth Banach space E. Let R be a retraction from E onto D. Then R is sunny and generalized nonexpansive if and only if 〈 x − Rx, JRx − Jy ≥ 0, 2.2 for all x ∈ E and y ∈ D. A generalized resolvent Jr of a maximal monotone operator B ⊂ E∗ × E is defined by Jr I rBJ −1 for any real number r >...