Sentence examples for mixed monotonicity of from inspiring English sources
By the mixed monotonicity of, we have.
Then from the mixed monotonicity of operator, we have (2.25).
By the mixed monotonicity of and (3.20), we have (3.31).
Then from the mixed monotonicity of, it follows that (3.6).
Hence, combining (3.4) with the mixed monotonicity of, we have (3.26) .
It follows from (3.14), (3.18), and the mixed monotonicity of that (3.20).
In this paper, we establish the existence of solutions to systems of Hammerstein integral inclusions under mixed monotonicity type conditions.
For example, Vishnevskiĭ [9] studied the behavior at large time of solutions to mixed problems for weakly connected cooperative parabolic systems and obtained the monotonicity of the solutions.
Lakshimikantham and Ćirić [4] extended the results in [3] by defining the mixed g-monotonicity and studied the existence and uniqueness of coupled coincidence point for such a mappings which satisfy the mixed monotone property in partially ordered metric spaces.
Lakshimikantham and Ćirić [7] extended the results in [6] by defining the mixed g-monotonicity and proved the existence and uniqueness of coupled coincidence point for such a mapping which satisfy the mixed monotone property in partially ordered metric spaces.
As a continuation of this trend, Lakshimikantham and Ćirić [7] extended the results in [6] by defining the mixed g-monotonicity and studied the existence and uniqueness of a coupled coincidence point for such mappings which satisfy the mixed monotone property in partially ordered metric spaces.
