A quantitative nonlinear strong ergodic theorem for Hilbert spaces

Strong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.

A quantitative Mean Ergodic Theorem for uniformly convex Banach spaces

We provide an explicit uniform bound on the local stability of ergodic averages in uniformly convex Banach spaces. Our result can also be viewed as a finitary version in the sense of T. Tao of the Mean Ergodic Theorem for such spaces and so generalizes similar results obtained for Hilbert spaces by Avigad, Gerhardy and Towsner [1] and T. Tao [11].

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Non-linear ergodic theorems in complete non-positive curvature metric spaces

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

Fixed point theorem and nonlinear complementarity problem in Hilbert spaces

In this paper, the concept of the strongly monotone type mapping is introduced, which contains the strongly monotone mapping and firmly type nonexpansive mapping as special cases. We show the equivalence between the fixed point problem and the complementarity problem of strongly monotone type mapping. Furthermore, it is obtained that an iteration sequence strongly converges to a unique solution...