for all x, y ∈ K . Let F(T) = {x ∈ K : Tx = x} be denoted as the set of fixed points of a mapping T . The first nonlinear ergodic theorem was proved by Baillon [1] for general nonexpansive mappings in Hilbert space : ifK is a closed and convex subset of and T has a fixed point, then for every x ∈ K , {Tnx} is weakly almost convergent, as n→∞, to a fixed point of T . It was also shown by Pazy [7...

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variationallike inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalizedmixed quasi-variational-like inequalities and so on. Bymeans of fixed point the...

The problem of how to merge, by means of a function, a family of metrics into a single one was studied deeply by J. Borsík and J. Doboš [On a product of metric spaces, Math. Slovaca 31 (1981) 193–205]. Motivated by the utility of quasi-metrics in Computer Science, the Borsík and Doboš study was extended to the quasi-metric context in such a way that a general description of how to combine throu...

Taking the standard parametrization of three-flavor neutrino mixing, we carefully examine the evolution of three CP-violating phases (δ, α1, α2) with energy scales in the realistic limit θ13 → 0. If m3 vanishes, we find that the one-loop renormalization-group equation (RGE) of δ does not diverge and its running has no quasi-fixed point. When m3 6= 0 holds, we show that the continuity condition ...

Smooth convex optimization problems are solved over fixed point sets of quasi-nonexpansive mappings by using a distributed optimization technique. This is done for a networked system with an operator, who manages the system, and a finite number of users, by solving the problem of minimizing the sum of the operator’s and users’ differentiable, convex objective functions over the intersection of ...