Abstract
A matrix approach to approximating solutions of variational inequalities in Hilbert spaces is introduced. This approach uses two matrices: one for iteration process and the other for regularization. Ergodicity and convergence (both weak and strong) are studied. Our methods combine new or well-known iterative methods (such as the original Mann’s method) with regularized processes involved regular matrices in the sense of Toeplitz.
Notes
No potential conflict of interest was reported by the authors.
1 However, we can find a wide study on quasi-nonexpansivity and some convergence results in Dotson [Citation8] and Senter and Dotson [Citation9].
2 for instance nonexpansive mappings, firmly nonexpansive mappings, pseudocontractive mappings, strictly pseudoconctractive mappings and so on.
3 for instance, Hilbert spaces, uniformly convex Banach spaces, uniformly smooth Banach spaces and so on.