A convergence result on random products of mappings in metric trees

作者：Al Mezel Saleh Abdullah^*; Khamsi Mohamed Amine

来源：Fixed Point Theory and Applications, 2012, 2012(1): 57.

DOI：10.1186/1687-1812-2012-57

• computerized tomography
• convex feasibility problem
• convex programming
• metric tree
• nonexpansive mapping
• projection algorithm
• projective mapping
• random product
• signal processing
• unrestricted iteration
• unrestricted product

Let X be a metric space and {T (1), ..., T (N) } be a finite family of mappings defined on D aS, X. Let r : a%26quot;center dot -%26gt; {1,..., N} be a map that assumes every value infinitely often. The purpose of this article is to establish the convergence of the sequence (x (n) ) defined by %26lt;br%26gt;x(0) is an element of D; and x(n+1) = T-r(n)(x(n)), for all n %26gt;= 0. %26lt;br%26gt;In particular we prove Amemiya and Ando%26apos;s theorem in metric trees without compactness assumption. This is the first attempt done in metric spaces. These type of methods have been used in areas like computerized tomography and signal processing.

• 出版日期2012