Sentence examples for using a mixed monotone from inspiring English sources

In [25], Chen and Li introduced and studied a class of semilinear impulsive evolution equations in Banach spaces by using a mixed monotone iterative technique.

In Section 4, by using a mixed monotone method, we obtain some new uniqueness criteria for the singular boundary value problem (1.1 - 1.2).

end{cases} (1.3) They investigated a unique positive solution of problem (1.3) by using a fixed point theorem of a mixed monotone operator.

By using the fixed point theorem of a mixed monotone operator, a unique existence result of positive solution to the problem (1.3) was established.

Using the fact that F has a mixed monotone property, we have as in [13] x n ≼ x n + 1 and y n + 1 ≼ y n ∀ n ≥ 0. Open image in new window (2.4).

The purpose of this paper is to establish the coupled fixed-point theorems for nonlinear contraction mappings, which have a mixed monotone property by using the cone ball-metric.

The method which we used for the analysis in this paper is the fixed point theorem of a mixed monotone operator in cone.

Hence L has a mixed monotone property.

Firstly, we prove that A is a mixed monotone operator.

Then, since is a mixed monotone operator, we have (3.21).

Let F : X × X → X have a mixed monotone property.