Sentence examples for by applying the fixed from inspiring English sources

Feng et al. [25] considered the existence and multiplicity of positive solutions to boundary value problem (1.5) by applying the fixed point theory in a cone for strict set contraction operators.

In Section 3, based on the basic solution of the definite homogeneous fourth-order parabolic equation, by applying the fixed point theory we prove the existence, uniqueness, and pth moment exponential stability of hybrid stochastic fourth-order parabolic equations.

In [44], Kang et al. have improved and generalized the work of [34] by applying the fixed point theory in cone for a strict set contraction operator; they proved that there exist various results on the existence of positive solutions to a class of fourth-order singular boundary value problems with integral boundary conditions (1.2).

In the following, we will prove that the operator (Q C_{1-gamma }(J,E)rightarrow C_{1-gamma}(J,E)) has at least one fixed point by applying the fixed point theorem.

In the following, we will prove that the operator (Q C^{nu,mu }(J,E rightarrow C^{nu,mu }(J,E)) has at least one fixed point by applying the fixed point theorem with respect to a k-set-contractive operator.

By applying the fixed point alternative, there exists a unique mapping C : X → Y in the set Ω1 = {g ∈ Ω; d f, g) < ∞} such that C ( x ) = lim n → ∞ 8 n f x 2 n (2.14).

This curve will then be transformed into a surface by applying the Fix Hole module.

In this section, we discuss simulation results obtained by applying the fixed-share experts framework to estimate TCP's RTT and help set TCP's RTO timer.

In Section 3, by applying the fixed-point theorem, we obtain the uniqueness and existence of at least three positive solutions for the system (1.1).

In [18], by applying the fixed-point theorem due to Leggett Williams, the authors considered the existence of positive solutions for a system of fractional multi-point boundary value problem with p-Laplacian operator.

Particularly, when α is an integer and ∫ 0 1 x ( s ) d A ( s ) = μ x , where 0 < η < 1 and 0 < μηn-1< 1, the authors of [5 8] established the existence and multiplicity of positive solutions for the n th-order three-point BVP (1.1) by applying the fixed-point theorems on cones.