In this paper, we introduce a new modified block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-j-asymptotically nonexpansive mappings, the set of the variational inequality for an a-inverse-strongly monotone operator, and the set of solutions of a system of generalized mixed equilibrium problems. We obtain ...

The existence of common fixed points is established for three mappings where T is either generalized (f, g)-nonexpansive or asymptotically (f, g)-nonexpansive on a set of fixed points which is not necessarily starshaped. As applications, the invariant best simultaneous approximation results are proved. AMS subject classifications: 47H10, 54H25

Definition . Let T : C → C be a mapping. T is said to be total asymptotically nonexpansive if there exist sequences {μn}, {νn} with μn,νn →  as n → ∞ and a strictly increasing continuous function ψ : R → R with ψ() =  such that ‖Tnx – Tny‖ ≤ ‖x – y‖ +μnψ(‖x – y‖) + νn holds for all x, y ∈ C and all n ∈N. T is said to be total asymptotically quasi-nonexpansive if F(T) = ∅, there exist seque...

In this paper, we consider an iteration process to approximate a common random fixed point of a finite family of asymptotically quasi-nonexpansive random mappings in convex metric spaces. Our results extend and improve several known results in recent literature.

In this paper, weak and strong convergence of two-step iteration sequences to a common fixed point for a pair of a finite family of asymptotically nonexpansive mappings and a finite family of generalized nonexpansive multivalued mappings in a nonempty closed convex subset of uniformly convex Banach spaces are presented. The results obtained in this paper extend and improve some recent known res...