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...-expansive''), then <math>f</math> has a [[fixed point (mathematics)|fixed point]]. ...nsive map <math>f</math> has a unique asymptotic center, which is a fixed point of <math>f</math>. (An ''asymptotic center'' of a sequence <math>(x_k)_{k\i ...

...ed-point formula]] that relates a sum over the [[fixed point (mathematics)|fixed points]] of a holomorphic [[vector field]] of a compact complex manifold to ...' is an [[automorphism]] of a compact complex manifold ''M'' with isolated fixed points, then ...

...phic mapping becomes a [[contraction mapping]] to which the [[Banach fixed-point theorem]] can be applied. ...mapping ''f'' has a unique fixed point ''x'' in ''D'' and if ''y'' is any point in ''D'', the iterates ''f''^''n''(''y'') converge to ''x''. ...

...bset]] in a [[locally convex topological vector space]] has a common fixed point. This theorem is a key tool in one of the quickest proofs of amenability of ...math> in <math>S</math>. Then the mappings in <math>S</math> share a fixed point.{{sfn | Conway | 1990 | pp=151–152}} ...

...ics]], a '''discrete fixed-point''' is a [[fixed point (mathematics)|fixed-point]] for functions defined on finite sets, typically subsets of the integer gr ...iscrete fixed point analysis and its applications|journal=Journal of Fixed Point Theory and Applications|language=en|volume=6|issue=2|pages=351–371|doi=10.1 ...

...d by Teck-Cheong Lim,<ref name="Lim">T.C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc. '''60''' (1976), 179–182.</ref> and, soon after, un ...rotund metric spaces as defined by J. Staples.<ref>J. Staples, Fixed point theorems in uniformly rotund metric spaces, Bull. Austral. Math. Soc. '''14''' (1976 ...

...tle=A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points |journal=The Bulletin of Symbolic Logic |date=September 2003 |volume ...>, then every [[endomorphism ]]<math>g: B \rightarrow B</math> has a fixed point. That is, there exists a morphism <math> b : 1 \rightarrow B</math> (where ...

...ntrol]], and [[mathematical economics]].<ref>{{cite book|title=Fixed Point Theorems with Applications to Economics and Game Theory|last=Border|first=Kim C.|pub ...ty]] or [[measurable function|measurability]]. This is where the selection theorems come into action: they guarantee that, if ''F'' satisfies certain propertie ...

...niversity of Chicago]] with thesis ''The Fixed Point Index and Fixed Point Theorems for K-Set Contractions'' supervised by [[Felix Browder]].<ref>{{MathGenealo ...2-9904-1969-12213-5|title=The fixed point index and asymptotic fixed point theorems for <math>k</math>-set-contractions|year=1969|last1=Nussbaum|first1=Roger D ...

...at any point on the conjugate beam is equal to the bending moment at that point divided by [[Flexural rigidity|EI]].<ref>{{cite book |url=https://books.goo ...the same amount of computation as the [[Moment-Area Theorem|moment-area]] theorems to determine a beam's slope or deflection; however, this method relies only ...

...)|ring]] ''R'' is the [[subring]] of the [[fixed point (mathematics)|fixed point]]s of ''f'', that is, ...of invariants under the group generated by ''S''. In particular, the fixed-point subring of an automorphism ''f'' is the ring of invariants of the [[cyclic ...

* If ''C'' is the [[category of vector spaces]] over a fixed [[field (mathematics)|field]] ''k'', the dualizable objects are precisely t ...ategory of [[chain complex]]es of [[module (mathematics)|modules]] (over a fixed [[commutative ring]] ''R''), dualizable objects ''V'' in ''C'' are precisel ...

{{Short description|Complex Analysis, Fixed-points and Iterations of Holomorphic Mappings}} ...is a theorem in [[complex analysis]] and [[dynamical systems]] concerning fixed points and iterations of [[holomorphic mapping]]s of the [[unit disc]] in t ...

...58|doi-access=free }}</ref><ref name=Wutiphol2>{{Cite journal|title=Common fixed points for R-weakly commuting in fuzzy metric spaces ...rnal|title=A comparison of various noncommuting conditions in metric fixed point theory and their applications ...

...iscrete fixed point analysis and its applications|journal=Journal of Fixed Point Theory and Applications|language=en|volume=6|issue=2|pages=351–371|doi=10.1 ...} }. These are the integer points that are considered "nearby" to the real point ''y''. ...

Kleinian group and ''j'' is a parabolic element of ''G'' with fixed point ''w'', then there is a [[horoball]] based at ''w'' is used to prove that every element of ''G'' which does not have a fixed point at ''w'' moves the horoball entirely ...

...ely on [[dynamic programming]] as it facilitates the proof of existence of fixed points. The result is due to [[David Blackwell]] who published it <ref>[htt ...action mapping then we can use [[Banach fixed-point theorem|Banach's fixed-point theorem]], and conclude that there is indeed a solution to ({{EquationNote| ...

...ation in [[numerical analysis]] is to [[approximation theory]], where such theorems quantify the difficulty of approximating general functions by functions of ...decreasing sequence of real numbers tending to zero. Then there exists a point ''x'' in ''X'' such that the distance of ''x'' to ''V''_''i'' is ...

...ath>x_i=-1</math> and nonnegative when <math>x_i=1</math>. Then there is a point in the <math>n</math>-dimensional [[cube]] <math>[-1,1]^n</math> in which a ...ef>{{Rp|page=545}}<ref>{{citation |last=Dugundji |first=James |title=Fixed Point Theory |pages=xv+690 |year=2003 |series=Springer Monographs in Mathematics ...

...ondition is satisfied "with probability 1" or [[almost surely]] for random point sets, while it may easily be violated for real data, since these are often ...separable; in jargon, it is said that a linear classifier ''shatters'' any point set with <math>N\le d+1</math>. This limiting quantity is also known as the ...