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

Jean-Bernard Baillon, Stephen Simons
1992 Journal of combinatorial theory. Series A  
from X into Zd 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).  ... 
doi:10.1016/0097-3165(92)90046-w fatcat:qadu6cvmmjdmpju3kanbtnhtaq

An integer optimization problem for non-Hamiltonian periodic flows [article]

Álvaro Pelayo, Silvia Sabatini
2013 arXiv   pre-print
We 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.  ... 
arXiv:1307.6766v1 fatcat:6tyoapk4k5apfe7zko7qsui3uy

Convexity in Helly Graphs: Selection and Almost Fixed Point Properties for Multifunctions

Rueiher Tsaur, Michael B. Smyth
2006 Electronical Notes in Theoretical Computer Science  
In particular, we show that 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  ... 
doi:10.1016/j.entcs.2006.04.030 fatcat:j4xuyhnmurcyjbgmvgelds6ye4

A Fixed Point Theorem for Left Amenable Semi-Topological Semi Groups

2015 Journal of Physical Mathematics  
In this note, we extend 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 .  ... 
doi:10.4172/2090-0902.1000138 fatcat:asmhnhoxy5eq3ksfdbhhvvenaa

Common Fixed Points of Generalized Cocyclic Mappings in Complex Valued Metric Spaces

Mujahid Abbas, Manuel De la Sen, Talat Nazir
2015 Discrete Dynamics in Nature and Society  
We present 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  ... 
doi:10.1155/2015/147303 fatcat:kbqqe46o4nhcxfr5miyuxcqz2i

Fermat and the number of fixed points of periodic flows [article]

Leonor Godinho, Álvaro Pelayo, Silvia Sabatini
2014 arXiv   pre-print
Moreover, if the 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.  ... 
arXiv:1404.4541v1 fatcat:p2rkt2dxbbcqbjzhu6hge6z64e

Stability of Fixed Point Sets of a Class of Multivalued Nonlinear Contractions

Binayak S. Choudhury, Chaitali Bandyopadhyay
2015 Journal of Mathematics  
The members of the sequence are assumed to be multivalued 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.  ... 
doi:10.1155/2015/302012 fatcat:xbtbxct34bdp7byl4gc75c7qe4

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.  ... 

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.  ... 

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.  ... 

Solving Fixed-Point Problems with Inequality and Equality Constraints via a Non-Interior Point Homotopy Path-Following Method

Menglong Su, Yufeng Shang
2017 Mathematical Problems in Engineering  
In this paper, we provide a constructive proof of the general Brouwer 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  ... 
doi:10.1155/2017/3456834 fatcat:622kz2hl2jhtfcqhchfxcxxcwu

Fermat and the number of fixed points of periodic flows

Leonor Godinho, Álvaro Pelayo, Silvia Sabatini
2015 Communications in Number Theory and Physics  
If the 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.  ... 
doi:10.4310/cntp.2015.v9.n4.a1 fatcat:ow7nja2gyjbwjllh3qgkagxqce

Amenable semigroups of nonexpansive mappings on weakly compact convex sets [article]

Andrzej Wiśnicki
2016 arXiv   pre-print
We also extend the 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.  ... 
arXiv:1612.06270v1 fatcat:bwcs44izbbhm7lnbwndbynv5pa

The Baillon–Simons theorems

Rueiher Tsaur
2005 Discrete Mathematics  
In this paper, we give combinatorial proofs of Baillon 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.  ... 
doi:10.1016/j.disc.2004.08.034 fatcat:qmq2d5zdy5cujdg7tiardoivjy

Remarks on best approximation in R-trees

William Kirk, Bancha Panyanak
2009 Annales Universitatis Mariae Curie-Sklodowska. Sectio A. Mathematica  
We also obtain a common best approximation 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.  ... 
doi:10.2478/v10062-009-0012-z fatcat:i6bzxfmd6jgmbgge3763hzcdpi
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