Results 21 to 30 of about 5,440 (186)
Compositions and Averages of Two Resolvents: Relative Geometry of Fixed Points Sets and a Partial Answer to a Question by C. Byrne [PDF]
, 2010 We show that the set of fixed points of the average of two resolvents can be found from the set of fixed points for compositions of two resolvents associated with scaled monotone operators.
Bauschke, Heinz H., Wang, Xianfu
core +1 more source
On Firmly Nonexpansive Mappings [PDF]
Proceedings of the American Mathematical Society, 1991 The author proves the following. Let X be a uniformly convex Banach space, \(C=C_ 1\cup C_ 2\cup...\cup C_ n\) a union of nonempty, bounded, closed and convex subsets of X, and T: \(C\to C\) a mapping such that \[ \| Tx-Ty\| \leq \| (1-\lambda)(x-y)+\lambda (Tx-Ty)\| \quad (x,y\in C), \] for some \(\lambda\in (0,1)\). Then T has a fixed point in C.
openaire +2 more sources
Demiclosedness Principles for Generalized Nonexpansive Mappings [PDF]
Journal of Optimization Theory and Applications, 2020 Demiclosedness principles are powerful tools in the study of convergence of iterative methods. For instance, a multi-operator demiclosedness principle for firmly nonexpansive mappings is useful in obtaining simple and transparent arguments for the weak convergence of the shadow sequence generated by the Douglas-Rachford algorithm. We provide extensions
Sedi Bartz, Rubรฉn Campoy, Hung M. Phan
openaire +2 more sources
Abstract and Applied Analysis, 2010 Let E be a smooth Banach space with a norm โโ โ. Let ๐(๐ฅ,๐ฆ)=โ๐ฅโ2+โ๐ฆโ2โ2โจ๐ฅ,๐ฝ๐ฆโฉ for any ๐ฅ,๐ฆโ๐ธ, where โจโ ,โ โฉ stands for the duality pair and J is the normalized duality mapping.
Hiroko Manaka
doaj +1 more source
Averaged alternating reflections in geodesic spaces [PDF]
, 2013 We study the nonexpansivity of reflection mappings in geodesic spaces and apply our findings to the averaged alternating reflection algorithm employed in solving the convex feasibility problem for two sets in a nonlinear context.
Fernandez-Leon, Aurora, Nicolae, Adriana
core +2 more sources
Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces
Abstract and Applied Analysis, 2015 Let E be a smooth Banach space with a norm ยท. Let V(x,y)=x2+y2-2โx,Jy for any x,yโE, where ยท,ยท stands for the duality pair and J is the normalized duality mapping. We define a V-strongly nonexpansive mapping by V(ยท,ยท).
Hiroko Manaka
doaj +1 more source
On a Class of Generalized Nonexpansive Mappings
Mathematics, 2020 In our recent work we have introduced and studied a notion of a generalized nonexpansive mapping. In the definition of this notion the norm has been replaced by a general function satisfying certain conditions.
Simeon Reich, Alexander J. Zaslavski
doaj +1 more source
On the Weak Relatively Nonexpansive Multivalued Mappings in Banach Spaces
Abstract and Applied Analysis, 2012 In recent years, the definition of relatively nonexpansive multivalued mapping and the definition of weak relatively nonexpansive multivalued mapping have been presented and studied by many authors.
Yongfu Su
doaj +1 more source
On the Fixed-Point Set of a Family of Relatively Nonexpansive and Generalized Nonexpansive Mappings
Fixed Point Theory and Applications, 2010 We prove that the set of common fixed points of a given countable family of relatively nonexpansive mappings is identical to the fixed-point set of a single strongly relatively nonexpansive mapping.
Saejung Satit, Nilsrakoo Weerayuth
doaj +2 more sources
Approximation of Fixed Points of Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces
International Journal of Mathematics and Mathematical Sciences, 2011 We introduce a concept of weak Bregman relatively nonexpansive mapping which is distinct from Bregman relatively nonexpansive mapping. By using projection techniques, we construct several modification of Mann type iterative algorithms with errors and ...
Jiawei Chen +3 more
doaj +1 more source