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Strong convergence for asymptotical pseudocontractions with the demiclosedness principle in banach spaces
Springer Science and Business Media LLC - Tập 2012 - Trang 1-8 - 2012
The aim of this article is to give an answer to an interesting question proposed
in Zhou. At the end of his article, he remarked that it was of great interest to
extend his results to certain Banach spaces. So in this article, we extend the
demiclosedness principle from Hilbert spaces to Banach spaces. A strong
convergence theorem for asymptotical pseudo-contractions in Banach spaces is
establishe...
Fixed-point theorems for the sum of two operators under ω-condensing
Springer Science and Business Media LLC - Tập 2013 - Trang 1-13 - 2013
The purpose of this paper is to establish fixed-point theorems for the sum of
two operators A and B, where the operator A is assumed to be contractive with
respect to the measure of weak noncompactness, while B is an φ-nonlinear
contraction. In the last section, we apply such results to study the existence
of solutions to a nonlinear Hammerstein integral equation in space....
A new iteration scheme for a hybrid pair of generalized nonexpansive mappings
Springer Science and Business Media LLC - - 2014
Abstract In this paper, we construct an iteration scheme involving a hybrid pair
of nonexpansive mappings and utilize the same to prove some convergence
theorems. In the process, we remove a restricted condition (called end-point
condition) in Sokhuma and Kaewkhao’s results (Fixed Point Theory Appl.
2010:618767, 2010). Thus, our results generalized and improved several results
contained in Sokhuma...
A Note on Asymptotic Contractions
Springer Science and Business Media LLC - Tập 2007 - Trang 1-6 - 2006
We provide sufficient conditions for the iterates of an asymptotic contraction
on a complete metric space to converge to its unique fixed point, uniformly on
each bounded subset of .
On the orbits of -closure points of ultimately nonexpansive mappings
Springer Science and Business Media LLC - Tập 2006 - Trang 1-4 - 2006
Let be a closed subset of a Banach space and an ultimately nonexpansive
commutative semigroup of continuous selfmappings. If the -closure of is
nonempty, then the closure of the orbit of any -closure point is a commutative
topological group....
Approximating Fixed Points of Nonexpansive Nonself Mappings in CAT(0) Spaces
Springer Science and Business Media LLC - Tập 2010 Số 1
AbstractSuppose that "Equation missing" is a nonempty closed convex subset of a
complete CAT(0) space "Equation missing" with the nearest point projection
"Equation missing" from "Equation missing" onto "Equation missing". Let
"Equation missing" be a nonexpansive nonself mapping with "Equation missing".
Suppose that "Equation missing" is generated iteratively by "Equation missing",
"Equation missi...
Some coupled coincidence and common fixed point results for a hybrid pair of mappings in 0-complete partial metric spaces
Springer Science and Business Media LLC - - 2013
Fixed point theorems in a new type of modular metric spaces
Springer Science and Business Media LLC - Tập 2018 - Trang 1-10 - 2018
In this paper, considering both a modular metric space and a generalized metric
space in the sense of Jleli and Samet (Fixed Point Theory Appl. 2015:61, 2015),
we introduce a new concept of generalized modular metric space. Then we present
some examples showing that the generalized modular metric space includes some
kind of metric structures. Finally, we provide some fixed point results for both
c...
Applications of order-theoretic fixed point theorems to discontinuous quasi-equilibrium problems
Springer Science and Business Media LLC - - 2015
In this paper, we apply order-theoretic fixed point theorems and isotone
selection theorems to study quasi-equilibrium problems. Some existence theorems
of solutions to quasi-equilibrium problems are obtained on Hilbert lattices,
chain-complete lattices and chain-complete posets, respectively. In contrast to
many papers on equilibrium problems, our approach is order-theoretic and all
results obtai...
Roots of mappings from manifolds
Springer Science and Business Media LLC - Tập 2004 - Trang 1-35 - 2004
Assume that is a proper map of a connected -manifold into a Hausdorff,
connected, locally path-connected, and semilocally simply connected space , and
has a neighborhood homeomorphic to Euclidean -space. The proper Nielsen number
of at and the absolute degree of at are defined in this setting. The proper
Nielsen number is shown to a lower bound on the number of roots at among all
maps properly hom...
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