- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 2 Issue: 1
- On some midpoint-type algorithms.
On some midpoint-type algorithms.
Authors : Giuseppe Marino, Roberta Zaccone
Pages : 42-61
Doi:10.31197/atnaa.407069
View : 4 | Download : 1
Publication Date : 2018-03-25
Article Type : Other
Abstract :We introduce iterative methods approximating fixed points for nonlinear operators defined on infinite-dimensional spaces. The starting points are the Implicit and Explicit Midpoint Rules, which generate polygonal functions approximating a solution for an ordinary differential equation infinite-dimensional spaces. The purpose is to determine suitable conditions on the mapping and the underlying space, in order to get strong convergence of the generated sequence to a common solution of a fixed point problem and a variational inequality.Keywords : Nonexpansive mappings, quasi-nonexpansive mappings, iterative algorithms, fixed points, midpoint rules, viscosity approximation, p-uniformly convex Banach spaces.