As is known to all, the proverbial

fixed-point theorem of Banach has been widely used in many branches of mathematics and physics.

The primary object of study, which we shall call the

fixed-point set of f/p, is the coincidence set of the pair.

Kakutani, A generalization of Brouwer's

fixed-point theorem, Duke Math.

In recent years,

fixed-point theorems have attracted increasing attention and have been widely investigated by many authors (e.g., [1-4] and the references therein) because these theorems play important roles in mechanics, physics, differential equations, and so on.

Petrot, "Set-valued

fixed-point theorems for generalized contractive mappings without the Hausdorff metric," Applied Mathematics Letters, vol.

step function,

fixed-point, iteration map, Newton map, Halley map, sieve of Eratosthenes

In the

fixed-point iteration method for solving nonlinear equation f(x)=0, the equation is usually rewritten as

Stojiljkovic: Common

fixed-point results for nonlinear contractions in ordered partial metric spaces, Fixed Point Theory Appl., 2011, 2011:71.

Tarafdar, "An approach to

fixed-point theorems on uniform spaces," Transactions of the American Mathematical Society, vol.

The output of the thermocouple (in volts) can then be plotted against the known temperature of the

fixed-point cell as it is melting (or freezing), which gives a reference output against which the thermocouple readings can be calibrated.

The most convincing method is to convert the

fixed-point inputs into IEEE 754 floating point numbers first.