scholarly journals Compositions and convex combinations of asymptotically regular firmly nonexpansive mappings are also asymptotically regular

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Heinz H Bauschke ◽  
Victoria Martín-Márquez ◽  
Sarah M Moffat ◽  
Xianfu Wang
Keyword(s):  
Nonexpansive Mappings ◽  
Firmly Nonexpansive ◽  
Firmly Nonexpansive Mappings ◽  
Asymptotically Regular

scholarly journals Fixed point theorems for nonexpansive mappings on nonconvex sets in UCED Banach spaces

2002 ◽  
Vol 31 (4) ◽  
pp. 251-257 ◽  
Author(s):  
Wei-Shih Du ◽  
Young-Ye Huang ◽  
Chi-Lin Yen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Compact Convex ◽  
Nonexpansive Mappings ◽  
Finite Union ◽  
Uniformly Convex ◽  
Weakly Compact ◽  
Nonconvex Sets ◽  
Firmly Nonexpansive ◽  
Asymptotically Regular

It is shown that every asymptotically regular orλ-firmly nonexpansive mappingT:C→Chas a fixed point wheneverCis a finite union of nonempty weakly compact convex subsets of a Banach spaceXwhich is uniformly convex in every direction. Furthermore, if{T i}i∈Iis any compatible family of strongly nonexpansive self-mappings on such aCand the graphs ofT i,i∈I, have a nonempty intersection, thenT i,i∈I, have a common fixed point inC.

Shrinking projection methods for firmly nonexpansive mappings

2009 ◽  
Vol 71 (12) ◽  
pp. e1626-e1632 ◽  
Author(s):  
Koji Aoyama ◽  
Fumiaki Kohsaka ◽  
Wataru Takahashi
Keyword(s):  
Nonexpansive Mappings ◽  
Projection Methods ◽  
Firmly Nonexpansive ◽  
Firmly Nonexpansive Mappings ◽  
Shrinking Projection Methods

scholarly journals Quantitative analysis of a subgradient-type method for equilibrium problems

2021 ◽  
Author(s):  
Nicholas Pischke ◽  
Ulrich Kohlenbach
Keyword(s):  
Quantitative Analysis ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Metric Regularity ◽  
Rates Of Convergence ◽  
Type Method ◽  
Firmly Nonexpansive ◽  
Firmly Nonexpansive Mappings ◽  
Fixed Point Sets

AbstractWe use techniques originating from the subdiscipline of mathematical logic called ‘proof mining’ to provide rates of metastability and—under a metric regularity assumption—rates of convergence for a subgradient-type algorithm solving the equilibrium problem in convex optimization over fixed-point sets of firmly nonexpansive mappings. The algorithm is due to H. Iiduka and I. Yamada who in 2009 gave a noneffective proof of its convergence. This case study illustrates the applicability of the logic-based abstract quantitative analysis of general forms of Fejér monotonicity as given by the second author in previous papers.

Sign in / Sign up

Export Citation Format

Share Document