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A set of sufficient conditions which guarantee the existence of a point x⋆ such that f(x⋆) = x⋆ is called a "fixed point theorem". Many such theorems are named after well-known mathematicians and economists.
Sanjo Zlobec
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Stage comparison, fixed points, and least fixed points in Kripke–Platek environments
et T be Kripke–Platek set theory with infinity extended by the axiom (Beta) plus the schema that claims that every set-bounded Σ-definable monotone operator from the collection of all sets to Pow(a) for some set a has a fixed point.
Jäger, Gerhard
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Fixed points and coupled fixed points in partially ordered ν-generalized metric spaces
New fixed point and coupled fixed point theorems in partially ordered ν-generalized metric spaces are presented. Since the product of two ν-generalized metric spaces is not in general a ν-generalized metric space, a different approach is needed than in ...
Mortaza Abtahi +2 more
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On fixed points of permutations [PDF]
The number of fixed points of a random permutation of 1,2,...,n has a limiting Poisson distribution. We seek a generalization, looking at other actions of the symmetric group. Restricting attention to primitive actions, a complete classification of the limiting distributions is given.
Diaconis, Persi +2 more
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AbstractWe consider fixed point logics, i.e., extensions of first order predicate logic with operators defining fixed points. A number of such operators, generalizing inductive definitions, have been studied in the context of finite model theory, including nondeterministic and alternating operators. We review results established in finite model theory,
Dawar, Anuj, Gurevich, Yuri
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A counter example on common periodic points of functions
By a counter example we show that two continuous functions defined on a compact metric space satisfying a certain semi metric need not have a common periodic point.
Aliasghar Alikhani-Koopaei
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Weakly Compatible Maps and Fixed Points [PDF]
Here, the existence of fixed points for weakly compatible maps is studied. The results are new generalization of the results of [5]. Finally, we study the new common fixed point theorems.
Mosa Shahsavari +2 more
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Global Wilson–Fisher fixed points
The Wilson–Fisher fixed point with O(N) universality in three dimensions is studied using the renormalisation group. It is shown how a combination of analytical and numerical techniques determine global fixed points to leading order in the derivative ...
Andreas Jüttner +2 more
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Existence of Fuzzy Fixed Points and Common Fuzzy Fixed Points for
This article contains results of the existence of fuzzy fixed points of fuzzy mappings that satisfy certain contraction conditions using the platform of partial b-metric spaces. Some non-trivial examples are provided to authenticate the main results. The
Dur-e-Shehwar Sagheer +4 more
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In the context of abstract interpretation for languages without higher-order features we study the number of times a functional need to be unfolded in order to give the least fixed point. For the cases of total or monotone functions we obtain an exponential bound and in the case of strict and additive (or distributive) functions we obtain a quadratic ...
Hanne Riis Nielson, Flemming Nielson
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