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.