Multiple-set split feasibility problems for asymptotically pseudo-nonspreading mappings in Hilbert spaces

Abstract

We introduce a new class of asymptotically pseudononspreading mappings and demonstrate its relationship with the existing related families of mappings. Demiclosedness principle for the mappings as well as the convexity and closedness of its fixed point set are established. Furthermore, we propose and investigate a new iterative algorithm for solving multiple-set split feasibility problem for the new class of mappings. In particular, weak and strong convergence theorems for solving multiple-set split feasibility problem for a certain subclass of the new class of mappings in Hilbert spaces are proved and certain applications are given. The results presented in the paper extend and improve the results of Osilike and Isiogugu [1], Quan and Chang [2] and host of other corresponding related results in literature.