Approximate Fixed Point Sequences of an Evolution Family on a Metric Space

Abstract EN

In this article, we study the approximate fixed point sequence of an evolution family.

A family E=Ux,y;x≥y≥0 of a bounded nonlinear operator acting on a metric space M,d is said to be an evolution family if Ux,x=I and Ux,yUy,z=Ux,z for all x≥y≥z≥0.

We prove that the common approximate fixed point sequence is equal to the intersection of the approximate fixed point sequence of two operators from the family.

Furthermore, we apply the Ishikawa iteration process to construct an approximate fixed point sequence of an evolution family of nonlinear mapping.