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About 10,000 papers for “Fixed point”

Fixed point..

K. L. Bondar, A. B. Jadhao, S. T. Patil · 2014

Existence of mild solutions of initial value problem for nonlinear difference equation with nonlocal conditions is obtained. The proof relay on the fixed point theorem for compact mapping.

Cited by 0

Fixed point combinators as fixed points of higher-order fixed point generators

Andrew Polonsky · SHILAP Revista de lepidopterología · 2020

Corrado B\"ohm once observed that if $Y$ is any fixed point combinator (fpc), then $Y(\lambda yx.x(yx))$ is again fpc. He thus discovered the first "fpc generating scheme" -- a generic way to build new fpcs from old. Continuing this idea, define an $\textit{fpc generator}$ to be any sequence of terms $G_1,\dots,G_n$ such that \[ Y \in FPC \Rightarrow Y G_1 \cdots G_n \in FPC \] In this contribution, we take first steps in studying the structure of (weak) fpc generators. We isolate several robust classes of such generators, by examining their elementary properties like injectivity and (weak) constancy. We provide sufficient conditions for existence of fixed points of a given generator $(G_1,\cdots,G_n)$: an fpc $Y$ such that $Y = Y G_1 \cdots G_n$. We conjecture that weak constancy is a necessary condition for existence of such (higher-order) fixed points. This statement generalizes Statman's conjecture on non-existence of "double fpcs": fixed points of the generator $(G) = (\lambda yx.x(yx))$ discovered by B\"ohm. Finally, we define and make a few observations about the monoid of (weak) fpc generators. This enables us to formulate new a conjecture about their structure.

Cited by 0Open access

Fixed point combinators as fixed points of higher-order fixed point generators

Andrew Polonsky · Logical Methods in Computer Science · 2020

Corrado B\"ohm once observed that if $Y$ is any fixed point combinator (fpc), then $Y(\lambda yx.x(yx))$ is again fpc. He thus discovered the first "fpc generating scheme" -- a generic way to build new fpcs from old. Continuing this idea, define an $\textit{fpc generator}$ to be any sequence of terms $G_1,\dots,G_n$ such that \[ Y \in FPC \Rightarrow Y G_1 \cdots G_n \in FPC \] In this contribution, we take first steps in studying the structure of (weak) fpc generators. We isolate several robust classes of such generators, by examining their elementary properties like injectivity and (weak) constancy. We provide sufficient conditions for existence of fixed points of a given generator $(G_1,\cdots,G_n)$: an fpc $Y$ such that $Y = Y G_1 \cdots G_n$. We conjecture that weak constancy is a necessary condition for existence of such (higher-order) fixed points. This statement generalizes Statman's conjecture on non-existence of "double fpcs": fixed points of the generator $(G) = (\lambda yx.x(yx))$ discovered by B\"ohm. Finally, we define and make a few observations about the monoid of (weak) fpc generators. This enables us to formulate new a conjecture about their structure.

Cited by 0Open access

Fixed point constructions

CANTINI, ANDREA · Florence Research (University of Florence) · 2006

Self-reference is a useful technical device in logical and foundational
\ninvestigations and it is often the case that self-referential constructions
\ngive rise to fixed point theorems.
\nWe survey some applications thereof, mainly concerned with:
\n(I) type-free abstraction with contraction-free logic;
\n(II) theories of self-applicable operations based on combinatory logic and lambda calculus.
\nThe coda illustrates the non-trivial role of pure self-referential objects with an application to the constructive foundations of mathematics.
\nwith an application to the constructive foundations of mathematics.

Cited by 0

Fixed point sets.

Ward, L. E. · Project Euclid (Cornell University) · 1973

Cited by 0

FIXED POINT ALGEBRAS

C. Smoryisfski · 2013

Although self-reference in arithmetic was used to impressive effect by Gödel in 1930 (published in 1931) when he noted the sentence asserting its own unprovability to be unprovable, and although this use immediately appealed to philosophers and philosophical logicians, it has largely been ignored by mathematical logicians. Indeed, it is only in the 1970s that arithmetic selfreference has begun to be systematically studied and applied. One aspect of this study is algebraic. In simplest terms one can distinguish two types of self-reference—extensional and nonextensional. Extensional self-reference lends itself quite readily to algebraic description and modelling, with some types of extensional selfreference even being amenable to algebraic study. The purpose of the present paper is to expound upon this algebraic modelling, touching briefly on its successes and delineating roughly the limits to this success. The central notion of this exposition is that of a fixed point algebra. This notion is a new one—it is untested and, hence, of only provisional interest. But it does appear useful:

Cited by 0

Fixed Point Iteration

G. Germano, MAZZANTI, STEFANO · AirIuav (Università Iuav di Venezia) · 1992

Iteration seems to play a fundamental role in learning theory - as everywhere else. Since neurons need a rather long time to reach a stable state, Caianiello's Paradox suggests that special actions cause the iteration of state transitions until a stable neural state is reached. Now, a stable state is a fixed point for any transition function; so we may call the iteration above, we want to discuss, "fixed point iteration".

Cited by 0

Fixed-Point Number

National Cancer Institute · Definitions · 2020

Ope n Pe e r Re v ie w on Qe ios

Cited by 0Open access

Fixed point analysis.

Xiaoxi Li (255922), Xueru Cao (19758456), Jinyan Deng (22075587) et al. · Figshare · 2025

<div> Railway accidents pose a significant threat to the industry, necessitating enhanced research into railway transportation safety. This study integrated a public oversight framework into the existing safety governance structure of railway transport operators, utilizing a four-party evolutionary game model and system dynamics for enhancement. Simulations conducted with Vensim software demonstrate that increased public supervision increases safety operation rates and improves the safety-related productivity of auxiliary enterprises. However, uncertainties in the evolutionary strategy process were identified. To address equilibrium fluctuations, a dynamic reward-punishment mechanism was developed. The optimized system achieved a safety operation rate of 99.7%, enhanced the safety-related productivity of the auxiliary enterprises to 93.2%, and increased the public supervision rate to 87.2%. These findings indicate that effective public participation and dynamic incentives can significantly improve safety management and prevent losses in railway sectors, offering valuable theoretical and practical insights for global railway enterprises. </div>

Cited by 0Open access