On some midpoint-type algorithms.

Year 2018, Volume: 2 Issue: 1, 42 - 61, 25.03.2018

Giuseppe Marino , Roberta Zaccone

https://doi.org/10.31197/atnaa.407069

Cited By: 1

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.

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