Strong Convergence of a Unified General Iteration fork-Strictly Pseudononspreading Mapping in Hilbert Spaces

We introduce a unified general iterative method to approximate a fixed point ofk-strictly pseudononspreading mapping. Under some suitable conditions, we prove that the iterative sequence generated by the proposed method converges strongly to a fixed point of ak-strictly pseudononspreading mapping with an idea of mean convergence, which also solves a class of variational inequalities as an optimality condition for a minimization problem. The results presented in this paper may be viewed as a refinement and as important generalizations of the previously known results announced by many other authors.

SUATU KAJIAN TITIK TETAP PEMETAAN k-PSEUDONONSPREADING SEJATI DI RUANG HILBERT

Let C be a subset of a real Hilbert space H. Let T : H ! H be a strictlyk-pseudononspreading mapping with a nonempty xed point set. Let ! 2 [k; 1) be xed.Let fTigNi=1be N k-strictly pseudononspreading mappings. In this paper, we study therelationship between of a xed point set of a k-strictly pseudononspreading mapping andother forms of certain combinations of some k-strictly pseudononspreading mappings inHilbert space.

Multiple-Set Split Feasibility Problems forκ-Strictly Pseudononspreading Mapping in Hilbert Spaces

The purpose of this paper is to prove some weak and strong convergence theorems for solving the multiple-set split feasibility problems forκ-strictly pseudononspreading mapping in infinite-dimensional Hilbert spaces by using the proposed iterative method. The main results presented in this paper extend and improve the corresponding results of Xu et al. (2006), of Osilike et al. (2011), and of many other authors.