In real Hilbert spaces, let the CFPP indicate a common fixed-point problem of asymptotically nonexpansive operator and countably many operators, suppose that HVI VIP represent hierarchical variational inequality problem, respectively. We put forward Mann hybrid deepest-descent extragradient approach for solving with constraints. The proposed algorithms are on basis Mann’s iterative technique, v...

We study the asymptotic behavior of the sequence of the iterates for a nonexpansive mapping, defined on a suitable subset of a Banach space with Opial's condition. Some results are stated also for semigroups of nonexpansive mappings and for mappings of asymptotically nonexpansive type in uniformly convex Banach spaces with Opial's condition.

In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family {Tj}i=1 of asymptotically quasi Ij−nonexpansive mappings as well as a family of {Ij}j=1 of asymptotically quasi nonexpansive mappings in the framework of Banach spaces. The obtained results improve and generalize the corresponding results in the existin...

and Applied Analysis 3 It is an interesting problem to extend the above results to a strongly continuous semigroup of nonexpansive mappings and a strongly continuous semigroup of asymptotically nonexpansive mappings. Let S be a strongly continuous semigroup of nonexpansive self-mappings. In 1998 Shioji and Takahashi 11 introduced, in Hilbert space, the implicit iteration

We study convergences of Mann and Ishikawa iteration processes for mappings of asymptotically quasi-nonexpansive type in Banach spaces. 1. Introduction and preliminaries. Let D be a nonempty subset of a real Banach space X and T : D → D a nonlinear mapping. The mapping T is said to be asymptotically quasi-nonexpansive (see [5]) if F(T) = ∅ and there exists a sequence {k n } in [0, ∞) with lim n...

*Correspondence: [email protected] School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China Abstract In this paper, we prove the demiclosed principle for total asymptotically nonexpansive nonself mappings in hyperbolic spaces. Then we obtain convergence theorems of the mixed Agarwal-O’Regan-Sahu type iteration for total asymptotically nonexpansive non...

We introduce two modifications of the Mann iteration, by using the hybrid methods, for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings in a Hilbert space. Then, we prove that such two sequences converge strongly to a common element of the set of solutions of an equilibrium problem and the set of common fixed points of an infinite family of asy...

We study nearly equal and nearly convex sets, ranges of maximally monotone operators, and ranges and fixed points of convex combinations of firmly nonexpansive mappings. The main result states that the range of an average of firmly nonexpansive mappings is nearly equal to the average of the ranges of the mappings. A striking application of this result yields that the average of asymptotically r...