Dynamic String-Maximum Methods in Metric Spaces

Abstract

In this chapter we study the convergence of dynamic string-maximum methods for solving common fixed point problems in a metric space. Our main goal is to obtain an approximate solution of the problem in the presence of computational errors. We show that our dynamic string-maximum algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant. Moreover, for a known computational error, we find out what an approximate solution can be obtained and how many iterates one needs for this.