Sentence examples for by using fixed point from inspiring English sources

One may note this from Example 3.3 in Section 3. In addition, Bai and Ge [16] generalized the Leggett-Williams fixed point theorems by using fixed point index theory.

In this paper, by using fixed point index theory and a double fixed point theorem, we study the existence of many positive solutions for a class of second-order p-Laplacian boundary value problems with impulse on time scales.

By using fixed point index theory and the Krasonsel'skii fixed point theorem, the existence of one and/or two positive solutions is established.

by using fixed point index theory in a cone.

The results are obtained by using fixed point theorems.

Some new results are obtained by using fixed point theorems.

By using fixed point theorems, we derive sufficient criteria to ensure the existence of solutions.

A new result on the existence of a solution is established by using fixed point theorems.

By using fixed point theorems in cones, the existence criteria of multiple positive solutions are established.

This implies that (SFP) can be solved by using fixed point algorithms.

By using fixed point theorem combined with the diagonalization process, they obtained the existence of solutions.