Sentence examples for by using various fixed from inspiring English sources
Results on this topic are usually achieved by using various fixed point theorems and degree theory.
They established the existence theory for positive solutions by using various fixed point theorems [20, 21].
Results on this topic are usually achieved by using various fixed point theorems in cone; see [1 4] and references therein for details.
The existence and uniqueness of solutions of functional equations and system of functional equations arising in dynamic programming have been studied by using various fixed point theorems (see [12, 16, 17] and the references therein).
Afterwards, further analyses on the properties of solutions for the functional equations (1.1) and (1.2) and others have been studied by several authors in [3 7] and [8 11] by using various fixed point theorems and monotone iterative technique, where (1.2) are as follows: (1.2).
In the last few decades, many authors have studied the multi-point boundary value problems for linear and nonlinear ordinary differential equations by using various methods, such as Leray-Schauder fixed point theorem, coincidence degree theory, Krasnosel'skii fixed point theorem, the shooting method and Leggett-Williams fixed point theorem.
I capture the relative productivity term by using various combinations of education-experience-time fixed effects.
By using various methods and techniques, for example, fixed point theorems, the method of upper and lower solutions, coincidence degree theory, and critical point theory, a series of existence results of periodic solutions have been obtained; we refer the reader to [2 8] and references therein.
In the last decade, by using various techniques such as critical point theory, fixed point theory, topological degree theory and coincidence degree theory, a great deal of works have been done on the existence of solutions to boundary value problems of difference equations (see [1 7] and references therein).
Forty eight hours post-transfection, the medium was removed and cells were immediately fixed in 3.7 % paraformaldehyde, followed by immunofluorescence and immunostaining using various antibodies as described in Supplementary Materials and methods.
