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Almost-fixed-point and fixed-point theorems for discrete-valued maps

1992
*
Journal of combinatorial theory. Series A
*

from X into Zd

doi:10.1016/0097-3165(92)90046-w
fatcat:qadu6cvmmjdmpju3kanbtnhtaq
*and**fixed*-*point**theorems**for*segment-*valued*multifunctions from X into 9(Zd). ... We say that x E X is an*almost*-*fixed*-*point*off if In this paper, we show how some*fixed*-*point**theorems*from (nonlinear functional) analysis can be used to obtain*almost*-*fixed*-poi:nt*theorems**for*functions ... from X into Zd*and**fixed*-*point**theorems**for*segment-*valued*multifunctions from X into 9(Zd). ...##
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An integer optimization problem for non-Hamiltonian periodic flows
[article]

2013
*
arXiv
*
pre-print

We

arXiv:1307.6766v1
fatcat:6tyoapk4k5apfe7zko7qsui3uy
*point*out an integer optimization problem to find a lower bound B(n) on the number of equilibrium*points*of non-Hamiltonian symplectic periodic flows on manifolds M in C. ... As a consequence, we confirm in dimensions 2n in 8,10,12,14,18,20, 22 a conjecture*for*unitary manifolds made by Kosniowski in 1979*for*the subclass C. ... Mc-Duff*for*useful comments. AP was partially supported by an NSF CAREER DMS-1055897. ...##
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Convexity in Helly Graphs: Selection and Almost Fixed Point Properties for Multifunctions

2006
*
Electronical Notes in Theoretical Computer Science
*

In particular, we show that

doi:10.1016/j.entcs.2006.04.030
fatcat:j4xuyhnmurcyjbgmvgelds6ye4
*for*any positive number p, every Helly graph has the neighbourhood convexity p 2 -*almost**fixed**point*property*for*p-weak multifunctions;*and*any self-*mapping*neighbourhood convexity ... We then consider various neighbourhood-convexity*almost**fixed**point*properties*for*Helly graphs. ... to the connection*Fixed**points*of continuous functions ←→*Almost**fixed**points*of (many-*valued*) graph homomorphisms This "link" between*almost**fixed**point*properties of*discrete*structures*and**fixed**point*...##
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A Fixed Point Theorem for Left Amenable Semi-Topological Semi Groups

2015
*
Journal of Physical Mathematics
*

In this note, we extend

doi:10.4172/2090-0902.1000138
fatcat:asmhnhoxy5eq3ksfdbhhvvenaa
*and*improve the corresponding result of Takahashi [1969.*Fixed**point**theorem**for*amenable semigroup of non-expansive*mappings*, Kodai Math. Sem. Rep. 21, 383-386]. ... Therefore contains only one*point*which is a common*fixed**point**for*the action of . ∎ Obviously every amenable*discrete*semigroup is a left amenable semi-topological semigroup, so we can apply*theorem*...*For*any non-empty compact convex subset of a Banach space , each commuting family of non-expansive self*mappings*on has a common*fixed**point*in . ...##
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Common Fixed Points of Generalized Cocyclic Mappings in Complex Valued Metric Spaces

2015
*
Discrete Dynamics in Nature and Society
*

We present

doi:10.1155/2015/147303
fatcat:kbqqe46o4nhcxfr5miyuxcqz2i
*fixed**point*results of*mappings*satisfying generalized contractive conditions in complex*valued*metric spaces. ... As an application, we obtain a common*fixed**point*of a pair of weakly compatible*mappings*. ...*Discrete*Dynamics in Nature*and*Society ...##
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Fermat and the number of fixed points of periodic flows
[article]

2014
*
arXiv
*
pre-print

Moreover, if the

arXiv:1404.4541v1
fatcat:p2rkt2dxbbcqbjzhu6hge6z64e
*fixed**point*set is*discrete*, we prove divisibility properties*for*the number of*fixed**points*, improving similar statements obtained by Hirzebruch in 1999. ... We obtain a general lower bound*for*the number of*fixed**points*of a circle action on a compact*almost*complex manifold M of dimension 2n with nonempty*fixed**point*set, provided the Chern number c_1c_n- ... that the*fixed**point*set is*discrete*. ...##
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Stability of Fixed Point Sets of a Class of Multivalued Nonlinear Contractions

2015
*
Journal of Mathematics
*

The members of the sequence are assumed to be multivalued

doi:10.1155/2015/302012
fatcat:xbtbxct34bdp7byl4gc75c7qe4
*almost*contractions. We show that the*fixed**point*sets of this sequence of*mappings*are stable. ... We consider a problem of stability of*fixed**point*sets*for*a sequence of multivalued*mappings*defined on a metric space converging to a limit function where the convergence is with respect to the Pompeiu-Hausdorff ... One of the reasons behind this is that multivalued*mappings*often have more*fixed**points*than their single*valued*counterparts.*For*instance, in the*theorem*of Nadler Jr. ...##
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Page 5519 of Mathematical Reviews Vol. , Issue 2004g
[page]

2004
*
Mathematical Reviews
*

Specific appli-
refined structures

*and*cations developed are a ‘digital convexity’ (*discrete*) version of Kakutani’s*fixed**point**theorem**for*convex-*valued*multifunctions,*and**fixed**point*properties of dendrites ... The link between*almost**fixed**point*properties of*discrete*structures*and**fixed**point*properties of spaces. (English summary) On formal description of computations new trends (Cork, 2000). Appl. ...##
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Page 2294 of Mathematical Reviews Vol. , Issue 80F
[page]

1980
*
Mathematical Reviews
*

The author defines a general notion of contraction

*for*set-*valued**mappings*of a metric space into itself*and*proves*fixed*-*point**theorems**for*such*mappings*of compact complete metric spaces, In the latter ... Achari, J. 80f:54041 Some*fixed**point**theorems**for*a class of*mappings*. Mat. Vesnik 2(15)(30) (1978), no. 2, 161-165. ...##
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Page 4471 of Mathematical Reviews Vol. , Issue 89H
[page]

1989
*
Mathematical Reviews
*

Some

*fixed**point**theorems**for*the first class of*maps*are given*and*a number of convergence properties (weak convergence*and*strong convergence) of the sequences of iterates*for*the second class of*maps*... Finally, the authors discuss a*fixed**point**theorem**for*locally nonexpansive*mappings*on (X¥ @Y).o. A. J. B. ...##
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Solving Fixed-Point Problems with Inequality and Equality Constraints via a Non-Interior Point Homotopy Path-Following Method

2017
*
Mathematical Problems in Engineering
*

In this paper, we provide a constructive proof of the general Brouwer

doi:10.1155/2017/3456834
fatcat:622kz2hl2jhtfcqhchfxcxxcwu
*fixed*-*point**theorem**and*then obtain the existence of a smooth path which connects a given*point*to the*fixed**point*. ... In recent years,*fixed*-*point**theorems*have attracted increasing attention*and*have been widely investigated by many authors. Moreover, determining a*fixed**point*has become an interesting topic. ... C20150027),*and*Innovation Scientists ...##
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Fermat and the number of fixed points of periodic flows

2015
*
Communications in Number Theory and Physics
*

If the

doi:10.4310/cntp.2015.v9.n4.a1
fatcat:ow7nja2gyjbwjllh3qgkagxqce
*fixed**point*set is*discrete*, we also prove divisibility properties*for*the number of*fixed**points*, improving similar statements obtained by Hirzebruch in 1999. ... We compute explicit lower bounds*for*the number of*fixed**points*of a circle action on a compact*almost*complex manifold M 2n with nonempty*fixed**point*set, provided the Chern number c 1 c n−1 [M ] vanishes ... Fermat*and*the number of*fixed**points*of periodic flows 679 The result*for*even*values*of n then follows from*Theorem*A. ...##
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Amenable semigroups of nonexpansive mappings on weakly compact convex sets
[article]

2016
*
arXiv
*
pre-print

We also extend the

arXiv:1612.06270v1
fatcat:bwcs44izbbhm7lnbwndbynv5pa
*fixed**point**theorem*of R. Hsu from left reversible*discrete*semigroups to left amenable semitopological semigroups in Banach spaces. ... We show a few*fixed**point**theorems**for*semigroups acting on weakly compact convex subsets of Banach spaces when LUC(S), AP(S), WAP(S) or WAP(S)∩ LUC(S) have a left invariant mean. ... Moreover, we obtain the*fixed**point**theorems**for*semigroups of nonexpansive*mappings*when LUC(S) or W AP (S) ∩ LUC(S) have a left invariant mean. ...##
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The Baillon–Simons theorems

2005
*
Discrete Mathematics
*

In this paper, we give combinatorial proofs of Baillon

doi:10.1016/j.disc.2004.08.034
fatcat:qmq2d5zdy5cujdg7tiardoivjy
*and*Simons'*almost**fixed**point**and**fixed**point**theorems**for**discrete*-*valued**mappings*(J. Combin. Theory Ser. A 60 (1992) 147-154). ... Acknowlegdment The author would like to thank Graham Brightwell of London School of Economics*and*Michael B. ... Smyth of Imperial College*for*many valuable suggestions which led to substantial improvements. ...##
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Remarks on best approximation in R-trees

2009
*
Annales Universitatis Mariae Curie-Sklodowska. Sectio A. Mathematica
*

We also obtain a common best approximation

doi:10.2478/v10062-009-0012-z
fatcat:i6bzxfmd6jgmbgge3763hzcdpi
*theorem**for*a commuting pair of*mappings*t : X → Y*and*T : X → 2 Y where t is single-*valued*continuous*and*T is ε-semicontinuous. 2000 Mathematics Subject Classification ... It is shown here that if T is an εsemicontinuous*mapping*whose*values*are nonempty closed convex subsets of Y,*and*if T has at least two distinct*points*of best approximation, then T must have a*fixed*... The research of the first author was supported in part by the Research Center*for*Nonlinear Analysis*and**Discrete*Mathematics at the National Sun Yat-sen University. ...
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