A convergence result on random products of mappings in metric spaces

作者：Khamsi Mohamed Amine^*; Louhichi Issam

来源：Fixed Point Theory and Applications, 2012, 43.

DOI：10.1186/1687-1812-2012-43

• computerized tomography
• convex feasibility problem
• convex programming
• Fejer monotone sequence
• image reconstruction
• image recovery
• innate bounded regularity
• Kaczmarz%26apos
• s method
• nonexpansive mapping
• projection algorithm
• projective mapping
• random product
• signal processing
• unrestricted iteration
• unrestricted product%26apos

Let be a metric space and {T-1, ..., T-N} be a finite family of mappings defined on D subset of X. Let r: N -%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 extend the study of Bauschke [1] from the linear case of Hilbert spaces to metric spaces. Similarly we show that the examples of convergence hold in the absence of compactness. These type of methods have been used in areas like computerized tomography and signal processing.

• 出版日期2012
• 单位中国石油大学（北京）