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Constant Limit of a Sequence of Iterates
SIAM Journal on Mathematical Analysis, 1979Let N be the set of all points on the complex sphere $\sigma $ at which a sequence F of iterates of a meromorphic function f is normal. N is shown to be exactly those points in some neighborhood of which F breaks down uniformly into a finite number of fixed subsequences. Consider any domain $D \subseteq N$ together with all its images under $f:F(D) = \{
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2002
AbstractThis chapter discusses the contradiction in the limits of iteration, one of the four limits of thought. This type of limit arises when there is some operation that is applied over and over again as far as possible. The most notable example is the mathematical (ordinal) infinite.
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AbstractThis chapter discusses the contradiction in the limits of iteration, one of the four limits of thought. This type of limit arises when there is some operation that is applied over and over again as far as possible. The most notable example is the mathematical (ordinal) infinite.
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Applied Numerical Mathematics, 1988
Let X be a complete metric space. For \(n=1,2,3,...\), let \(f_ n\) be a function \(X\to X\) having a unique fixed point \(\alpha_ n\). Write \(F_ n=f_ 1\circ f_ 2\circ...\circ f_ n\). Under suitable conditions, there is an \(\alpha\in X\) such that, for each \(x\in X\), we have \(F_ n(x)\to \alpha\) as \(n\to \alpha\).
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Let X be a complete metric space. For \(n=1,2,3,...\), let \(f_ n\) be a function \(X\to X\) having a unique fixed point \(\alpha_ n\). Write \(F_ n=f_ 1\circ f_ 2\circ...\circ f_ n\). Under suitable conditions, there is an \(\alpha\in X\) such that, for each \(x\in X\), we have \(F_ n(x)\to \alpha\) as \(n\to \alpha\).
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1983
Nach der Einleitung des Verf. handelt es sich um den von Pringsheim, London u.a. behandelten Problemkreis der Limesexistenz bei mehrfachen Folgen. Der Abschnitt II ist trivial. Abschnitt I bedarf erst einer Beseitigung sinnstörender Druckfehler und sonstiger Unklarheiten (S. 42 notwendig und hinreichend verwechselt; S. 42, Z. 1 und 2 unklar; S.
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Nach der Einleitung des Verf. handelt es sich um den von Pringsheim, London u.a. behandelten Problemkreis der Limesexistenz bei mehrfachen Folgen. Der Abschnitt II ist trivial. Abschnitt I bedarf erst einer Beseitigung sinnstörender Druckfehler und sonstiger Unklarheiten (S. 42 notwendig und hinreichend verwechselt; S. 42, Z. 1 und 2 unklar; S.
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The limit points of affine iterations
Numerical Functional Analysis and Optimization, 1990Suppose the mapping T has more then one fixed point. If the iteration converges, the limit will depend on the choice of the starting point. It is shown that for affine mappings this dependency can be described by solutions of certain linear equations.
Peter Kosmol, Xinlong Zhou
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Methods and limits of iterative multiuser decoding
Proceedings 2001 IEEE Information Theory Workshop (Cat. No.01EX494), 2002Previous work has identified iterative multiuser decoding techniques that are often only limited by theoretical channel capacity. These investigations usually dealt with the case where user waveforms are decorrelated to some degree. Investigations with identical waveforms indicate that the theoretical capacity limits are not always achieved ...
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Iterated Limiting Recursion and the Program Minimization Problem
Journal of the ACM, 1974The general problem of finding minimal programs realizing given “program descriptions” is considered, where program descriptions may be of finite or infinite length and may specify arbitrary program properties. The problem of finding minimal programs consistent with finite or infinite input-output lists is a special case (for infinite ...
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AN ITERATED LIMITS THEOREM APPLIED TO THE HENSTOCK INTEGRAL
Real Analysis Exchange, 1995Russell A Gordon
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Ratio limits and simulation algorithms for the Palm version of stationary iterated tessellations
Journal of Statistical Computation and Simulation, 2014Volker Schmidt +2 more
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