Asymptotic behavior of nonexpansive mappings in normed linear spaces

1981 ◽  
Vol 38 (4) ◽  
pp. 269-275 ◽  
Author(s):  
Elon Kohlberg ◽  
Abraham Neyman
Keyword(s):  
Asymptotic Behavior ◽  
Nonexpansive Mappings ◽  
Linear Spaces ◽  
Normed Linear Spaces

scholarly journals Contractibility of Fixed Point Sets of Mean-Type Mappings

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
S. Iampiboonvatana ◽  
P. Chaoha
Keyword(s):  
Fixed Point ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Point Sets ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Convex Setting ◽  
Fixed Point Sets

We establish a convergence theorem and explore fixed point sets of certain continuous quasi-nonexpansive mean-type mappings in general normed linear spaces. We not only extend previous works by Matkowski to general normed linear spaces, but also obtain a new result on the structure of fixed point sets of quasi-nonexpansive mappings in a nonstrictly convex setting.

scholarly journals Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Mujahid Abbas ◽  
Basit Ali ◽  
Salvador Romaguera
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Contractive Mapping ◽  
Linear Spaces ◽  
Complete Metric Spaces ◽  
Normed Linear Spaces ◽  
Fixed Point Result ◽  
Invariant Approximation ◽  
New Type

Wardowski (2012) introduced a new type of contractive mapping and proved a fixed point result in complete metric spaces as a generalization of Banach contraction principle. In this paper, we introduce a notion of generalizedF-contraction mappings which is used to prove a fixed point result for generalized nonexpansive mappings on star-shaped subsets of normed linear spaces. Some theorems on invariant approximations in normed linear spaces are also deduced. Our results extend, unify, and generalize comparable results in the literature.

An orthogonality in normed linear spaces based on angular distance inequality

2015 ◽  
Vol 90 (2) ◽  
pp. 281-297 ◽  
Author(s):  
F. Dadipour ◽  
F. Sadeghi ◽  
A. Salemi
Keyword(s):  
Angular Distance ◽  
Linear Spaces ◽  
Normed Linear Spaces
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