A GENERAL ITERATIVE SCHEME FOR STRICT PSEUDONONSPREADING MAPPING RELATED TO OPTIMIZATION PROBLEM IN HILBERT SPACES

Abstract

In this paper, we introduce a general iterative scheme for finding fixed points of a strictly pseudononspreading mapping. We show that, under some suitable conditions, the sequence which is generated by the proposed iterative scheme converges strongly to a fixed point of the mapping. Moreover, such a fixed point is a solution of a certain optimization problem that induced by a strongly positive bounded linear operator. Consequently, since the class of strictly pseudononspreading mapping is the largest one, the main results presented in this paper extend various results existing in the current literature.