Round-off stability for multi-valued maps

Abstract

An iterative procedure for a map T is said to be stable if the approximate sequence arising in numerical praxis converges to the point anticipated by the theoretical sequence. The study of stability of iterative procedures plays a vital role in computational analysis, game theory, computer programming, and fractal geometry. In generation of fractals, a sequence of approximations produces a stable set attractor only if the corresponding iterative procedure shows a stable behavior. The purpose of this article is to discuss stability of the Picard iterative procedure for a map T satisfying Zamfirescu multi-valued contraction on a metric space. © 2012 Singh et al; licensee Springer.