The phrase "fixed point argument" is grammatically correct and is commonly used in mathematics and other fields.
It refers to a specific type of mathematical proof commonly used to establish the existence of a fixed point, which is a point that remains unchanged under a given operation. You can use this phrase whenever discussing or describing a mathematical proof involving fixed points. For example: "The proof of the Banach fixed point theorem relies heavily on the use of a fixed point argument." "By using a fixed point argument, we can show that this function has at least one fixed point." "In this paper, we will present a novel fixed point argument for solving nonlinear equations."
Indeed, under the previous assumption, the system can be written G ¯ ( W ) = − κ W + F ( W ), where F is a contraction operator on E 1 3. Therefore, one can prove the uniqueness of the fixed point with the Banach fixed point argument and exhibit an energy function for the system.
We present two approaches to prove existence of solutions on bounded domains: via minimization of an indefinite functional and via a fixed point argument.
The proof of (mathrm{(iii)}) follows from a standard contraction mapping fixed point argument, details are omitted.
By exploiting the exact controllability of the unperturbed linear third-order dispersion equation, and by applying the classical contraction mapping fixed point argument, we proved under the condition that the nonlinearity is weak that the semilinear dispersion equation in question is still exactly controllable.
The proof is based on a fixed point argument, via the Mönch fixed point theorem, using the Hausdorff measure of non-compactness.
Using the semigroup theory and fixed point argument, we establish a set of sufficient conditions for obtaining the required result.
Then fixed point arguments are used to obtain the desired solution of associated nonlinear problems.
The main tools used in the literature for such a problem are the coincidence degree theory of Mawhin, fixed point arguments together with the lower and upper solutions method.
Concretely,our main purpose is to prove that the Baire partial quasi-metric space is an appropriatemathematical framework for discussing via fixed point arguments the asymptotic complexityof a general class of recursive algorithms to which all the algorithms analyzed inCerdà-Uguet et al. (Theory Comput. Syst.
By advanced techniques, based on the Lefschetz-type fixed point theorems and sophisticated degree arguments (fixed point index techniques), we are able to treat not only the sole existence problems, but also to guarantee certain sorts of a weak stability called nonejectivity and essentiality.
In [2, 5, 6], the authors used fixed point theory or topological degree argument.
