Open AccessFixed points of a new class of pseudononspreading mappings
Author(s) -
M.O. Osilike,
F. O. Isiogugu,
P. U. Nwokoro,
E. E. Chima,
O. U. Oguguo
Publication year - 2019
Publication title -
analele universităţii din timişoara. seria matematică-informatică/analele universităţii de vest din timişoara. seria matematică-informatică
Language(s) - English
Resource type - Journals
eISSN - 1841-3307
pISSN - 1841-3293
DOI - 10.2478/awutm-2019-0008
Subject(s) - class (philosophy) , mathematics , fixed point , regular polygon , hilbert space , pure mathematics , coincidence point , property (philosophy) , set (abstract data type) , convergence (economics) , nonlinear system , fixed point theorem , discrete mathematics , mathematical analysis , computer science , artificial intelligence , philosophy , physics , geometry , epistemology , quantum mechanics , economics , programming language , economic growth
We extend the notion of k-strictly pseudononspreading mappings introduced in Nonlinear Analysis 74 (2011) 1814-1822 to the notion of the more general pseudononspreading mappings . It is shown with example that the class of pseudononspreading mappings is more general than the class of k-strictly pseudonon-spreading mappings. Furthermore, it is shown with explicit examples that the class of pseudononspreading mappings and the important class of pseudocontractive mappings are independent. Some fundamental properties of the class of pseudononspreading mappings are proved. In particular, it is proved that the fixed point set of certain class of pseudononspsreading selfmappings of a nonempty closed and convex subset of a real Hilbert space is closed and convex. Demiclosedness property of such class of pseudonon-spreading mappings is proved. Certain weak and strong convergence theorems are then proved for the iterative approximation of fixed points of the class of pseudononspreading mappings.