On the role of the coefficients in the strong convergence of a general type Mann iterative scheme
Giuseppe Marino, Luigi Muglia · Journal of Inequalities and Applications · 2015
Let H be a Hilbert space. Let $(W_{n})_{n\in\mathbb{N}}$ be a suitable family of mappings. Let S be a nonexpansive mapping and D be a strongly monotone operator. We study the convergence of the general scheme $x_{n+1}=W_{n}(\alpha_{n}Sx_{n}+(1-\alpha_{n})(I-\mu_{n}D)x_{n}) $ in dependence on the coefficients $(\alpha_{n})_{n\in\mathbb{N}}$ , $(\mu_{n})_{n\in\mathbb{N}}$ .