# fixed point

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## fixed point

[¦fikst ′pȯint]
(engineering)
A reproducible value, as for temperature, used to standardize measurements; derived from intrinsic properties of pure substances.
(mathematics)
For a function ƒ mapping a set S to itself, any element of S which ƒ sends to itself.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Fixed Point

a form of representation of numbers in a digital computer with constant position of the point that sepa-rates the whole part of the number from the fraction. The fixed point corresponds to the natural form of representation of numbers. The point may be fixed at any position of the number—for example, in a digital computer five-place numbers with a fixed point after the second place are represented as +74.531, +07.453, +00.745, and so on. To prevent the numbers formed in the process of calculations from going beyond the range of representable numbers, scale factors are incorporated into the input data and intermediate and final results when drawing up programs for computers with a fixed point. However, the fixing of the point before the high-order digit of the modulus of the number (a number less than 1) is more expedient; in such a case the word format of the digital computer is not overloaded during multiplication of numbers. The range of representable numbers is narrower in a digital computer with a fixed point than in a digital computer with a floating point. The complication of programming when a fixed point is used is compensated in some cases by the simplicity of the devices of the digital computer and the ease in carrying out arithmetic operations, and also by the possibility of achieving greater speed in addition and subtraction. A fixed point was used in the Soviet Minsk-1, Setun’, and Ural-1 digital computers and in most digital control computers.

A. V. GUSEV

## fixed point

(mathematics)
The fixed point of a function, f is any value, x for which f x = x. A function may have any number of fixed points from none (e.g. f x = x+1) to infinitely many (e.g. f x = x). The fixed point combinator, written as either "fix" or "Y" will return the fixed point of a function.

## fixed point

A method for storing and calculating numbers in which the decimal point is always in the same location. Contrast with floating point.
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References in periodicals archive ?
Jungck, "Commuting maps and fixed points," The American Mathematical Monthly, vol.
Vetro, "Common fixed points in generalized metric spaces," Applied Mathematics and Computation, vol.
Vetro, "Common Fixed Points of a Pair of Hardy Rogers Type Mappings on a Closed Ball in Ordered Dislocated Metric Spaces," journal of function spaces and applications, vol.
Sahmim, "On common fixed points for [alpha]-[psi]-contractions and generalized cyclic contractions in b-metric-like spaces and consequences," Journal of Nonlinear Sciences and Applications, vol.
To do that, we consider iterative monoparametric maps that introduce these six fixed points. As a construction element of the dynamic rules, we use the following functions:
PARK and H.KIM, PCNS-SNU 18 (1993) --The first author introduced certain general classes of upper semicontinuous multimaps defined on convex spaces which were shown to be adequate to establish theories on fixed points, coincidence points, KKM maps, variational inequalities, best approximations, and many others.
Turning to set-valued analysis, they consider such topics as the Hausdorff metric and the distance between sets, upper and lower semi-continuous set-valued maps, fixed points and coincidences of maps in metric spaces, and topological degree and fixed points of set-valued maps in Banach spaces.
Fixed Points and Stability Analysis of the Autonomous System
Park, "Fixed points and quasi-equilibrium problems," Mathematical and Computer Modelling, vol.
The real fixed points of the operator are [x.sup.F.sub.1] = 0 and [x.sup.F.sub.2]([alpha], [gamma]), while the other two fixed points are complex.
A systematic study of the fixed point theory of the pair (f, p), by analogy with the theory of Vietoris fractions (see [13, Section 19]), was undertaken in , using the notation 'f/p ' for the pair considered as a fraction.

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