On some midpoint-type algorithms.

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Advances in the Theory of Nonlinear Analysis and its Application
Volume:2 Issue:1
On some midpoint-type algorithms.

On some midpoint-type algorithms.

Authors : Giuseppe MARİNO, Roberta Zaccone

Pages : 42-61

Doi:10.31197/atnaa.407069

View : 7 | Download : 7

Publication Date : 2018-03-25

Article Type : Review Paper

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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