Weak and Strong Convergence Theorems for Nonspreading type Mapping in a Hilbert Spaces

Abstract

The work of Osilike and Isiogugu, Nonlinear Analysis, 74 (2011), 1814-1822 on weak and strong convergence theorems for a new class of k-strictly pseudononspreading mappings in real Hilbert spaces is reviewed. We studied in detail this new class of mappings which is more general than the class of nonspreading mappings studied by Kurokawa and Takahashi, Nonlinear Analysis 73 (2010) 1562-1568. Many incisive examples establishing the relationship of the class of k-strictly pseudononspreading mappings and several other important classes of operators are presented. Interesting properties of k-strictly pseudononspreading mappings and weak and strong convergence theorems for approximation of its fixed points which appeared in the cited work of Osilike and Isiogugu were studied and presented.