Coupled solutions for a bivariate weakly nonexpansive operator by iterations

We prove weak and strong convergence theorems for a double Krasnoselskij type iterative method to approximate coupled solutions of a bivariate nonexpansive operator F : C x C --> C, where C is a nonempty closed and convex subset of a Hilbert space. The new convergence theorems generalize, extend, improve and complement very important old and recent results in coupled fixed point theory. Some appropriate examples to illustrate our new results and their generalization are also given.