Open AccessIterative Schemes for Fixed Points of Relatively Nonexpansive Mappings and Their Applications
Author(s) -
Somyot Plubtieng,
Wanna Sriprad
Publication year - 2010
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2010/301305
Subject(s) - mathematics , banach space , fixed point , hilbert space , variational inequality , monotone polygon , countable set , convergence (economics) , regular polygon , pure mathematics , weak convergence , discrete mathematics , mathematical analysis , computer security , economic growth , geometry , computer science , economics , asset (computer security)
We present two iterative schemes with errors which are proved to be strongly convergentto a common element of the set of fixed points of a countable family of relatively nonexpansive mappingsand the set of fixed points of nonexpansive mappings in the sense of Lyapunov functional in a real uniformlysmooth and uniformly convex Banach space. Using the result we consider strong convergence theorems forvariational inequalities and equilibrium problems in a real Hilbert space and strong convergence theoremsfor maximal monotone operators in a real uniformly smooth and uniformly convex Banach space
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