fixed point


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Related to fixed point: Fixed point number, Fixed point theorem

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.

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.

See also least fixed point.

fixed point

A method for storing and calculating numbers in which the decimal point is always in the same location. Contrast with floating point.
References in periodicals archive ?
gamma]] x K [right arrow] K of the S- action on K possesses a common fixed point in K which we denote by [x.
From Table 1, we know that there are many existing literatures involving fixed point technique and stability analysis, and a lot of interesting conclusions are derived [21-23, 28-30].
12] studied complex valued metric space and proved common fixed point theorems for two self-mappings satisfying a rational type inequality.
In this paper, we continue the study of fixed point theorems in complex valued b-metric spaces.
We prove fixed point theorems for such mappings on multiplicative metric space endowed with a graph G.
16] claimed that most of the coupled fixed point theorems in the setting of single valued mappings on ordered metric spaces are consequences of well-known fixed point theorems.
On the other hand, cycle insertion can only change the number of fixed points by [+ or -]1: it increases by 1 if n + 1 is inserted as a new fixed point, and decreases by 1 if j was previously a fixed point.
Yamada: The hybrid steepest-descent method for variational inequality problems over the intersection of the fixed point sets of nonexpansive mappings, Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, Edited by D.
If the fixed point is stable, or attractive, then small perturbations about [x.
In the present paper, we prove a common fixed point theorem for occasionally weakly compatible mappings in Menger space satisfying a new contractive type condition.
In this paper, our purpose is to show that the more general modified Mann iteration sequence with errors converges to the unique fixed point of T if T : X [right arrow] X is a uniformly continuous strongly successively pseudocontractive mapping with a bounded range or T : X [right arrow] X is uniformly Lipschitzian and strongly successively pseudocontractive mapping without necessarily having a bounded range.