617 research outputs found
Approximating fixed point of({\lambda},{\rho})-firmly nonexpansive mappings in modular function spaces
In this paper, we first introduce an iterative process in modular function
spaces and then extend the idea of a {\lambda}-firmly nonexpansive mapping from
Banach spaces to modular function spaces. We call such mappings as
({\lambda},{\rho})-firmly nonexpansive mappings. We incorporate the two ideas
to approximate fixed points of ({\lambda},{\rho})-firmly nonexpansive mappings
using the above mentioned iterative process in modular function spaces. We give
an example to validate our results
On Ray's theorem for weak firmly nonexpansive mappings in Hilbert Spaces
In this work, we introduce notions of generalized firmly nonexpansive (G-firmly non expansive) and fundamentally firmly nonexpansive (F-firmly nonexpansive) mappings and utilize to the same to prove Ray's theorem for G-firmly and F-firmly nonexpansive mappings in Hilbert Spaces. Our results extend the result due to F. Kohsaka [ Ray's theorem revisited: a fixed point free firmly nonexpansive mapping in Hilbert spaces, Journal of Inequalities and Applications (2015) 2015:86 ]
Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces
We further study averaged and firmly nonexpansive mappings in the setting of
geodesic spaces with a main focus on the asymptotic behavior of their Picard
iterates. We use methods of proof mining to obtain an explicit quantitative
version of a generalization to geodesic spaces of result on the asymptotic
behavior of Picard iterates for firmly nonexpansive mappings proved by Reich
and Shafrir. From this result we obtain effective uniform bounds on the
asymptotic regularity for firmly nonexpansive mappings. Besides this, we derive
effective rates of asymptotic regularity for sequences generated by two
algorithms used in the study of the convex feasibility problem in a nonlinear
setting
The Asymptotic Behavior of the Composition of Firmly Nonexpansive Mappings
In this paper we provide a unified treatment of some convex minimization
problems, which allows for a better understanding and, in some cases,
improvement of results in this direction proved recently in spaces of curvature
bounded above. For this purpose, we analyze the asymptotic behavior of
compositions of finitely many firmly nonexpansive mappings in the setting of
-uniformly convex geodesic spaces focusing on asymptotic regularity and
convergence results
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