Mosco convergence of the sets of fixed points for one-parameter nonexpansive semigroups

2008 ◽  
Vol 68 (12) ◽  
pp. 3870-3878 ◽  
Author(s):  
Tomonari Suzuki
Keyword(s):  
Fixed Points ◽  
Mosco Convergence ◽  
Nonexpansive Semigroups

scholarly journals Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li-Jun Zhu
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Linear Operators ◽  
Nonexpansive Semigroup ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Nonexpansive Semigroups

The purpose of the present paper is to study the hierarchical constrained variational inequalities of finding a pointx*such thatx*∈Ω,〈(A-γf)x*-(I-B)Sx*,x-x*〉≥0,  ∀x∈Ω, whereΩis the set of the solutions of the following variational inequality:x*∈Ϝ,〈(A-S)x*,x-x*〉≥0,  ∀x∈Ϝ, whereA,Bare two strongly positive bounded linear operators,fis aρ-contraction,Sis a nonexpansive mapping, andϜis the fixed points set of a nonexpansive semigroup{T(s)}s≥0. We present a double-net convergence hierarchical to some elements inϜwhich solves the above hierarchical constrained variational inequalities.

scholarly journals Approximation of fixed points for nonexpansive semigroups in Hilbert spaces

2013 ◽  
Vol 2013 (1) ◽  
pp. 31 ◽  
Author(s):  
Yonghong Yao ◽  
Jung Kang ◽  
Yeol Cho ◽  
Yeong-Cheng Liou
Keyword(s):  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Semigroups

scholarly journals Common fixed points of monotone ρ-nonexpansive semigroup in modular spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Noureddine El Harmouchi ◽  
Karim Chaira ◽  
El Miloudi Marhrani
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Common Fixed Points ◽  
Nonexpansive Semigroup ◽  
Iteration Algorithm ◽  
Uniformly Convex ◽  
Modular Spaces ◽  
Nonexpansive Semigroups ◽  
Convergence Results

Abstract In this paper, we consider the class of monotone ρ-nonexpansive semigroups and give existence and convergence results for common fixed points. First, we prove that the set of common fixed points is nonempty in uniformly convex modular spaces and modular spaces. Then we introduce an iteration algorithm to approximate a common fixed point for the same class of semigroups.

A Fixed Point Theorem for Semigroups of Proximately Uniformly Lipschitzian Mappings

1991 ◽  
Vol 34 (4) ◽  
pp. 559-562
Author(s):  
Hong-Kun Xu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Existence Theorem ◽  
Point Theorem ◽  
Common Fixed Points ◽  
Nonexpansive Semigroups ◽  
Lipschitzian Mappings ◽  
Lipschitzian Semigroup

AbstractAs a generalization of Kiang and Tan's proximately nonexpansive semigroups, the notion of a proximately uniformly Lipschitzian semigroup is introduced and an existence theorem of common fixed points for such a semigroup is proved in a Banach space whose characteristic of convexity is less than one.

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