Algebraic dependences of meromorphic mappings sharing few moving hyperplanes with truncated multiplicity

In this article, we will prove an algebraic dependence theorem for meromorphic mappings into a complex projective space sharing few moving hyperplanes with different truncated multiplicity. Moreover, we also consider the weaker condition: \ (₅, ₀㶁), kᵢ (₆, ₀㶁), kᵢ instead of (₅, ₀㶁), kᵢ= (₆, ₀㶁), kᵢ\ for some moving hyperplanes among the given moving hyperplanes. In order to implement this, besides using the technique reported by S. D. Quang in (Two meromorphic mappings having the same inverse images of some moving hyperplanes with truncated multiplicity, Rocky Mountain J. Math. , vol. 52, no. 1, pp. 263–273, 2022) we have to separate the 2n + 2 moving hyperplanes from the given p+1 moving hyperplanes. After that, we count multiples of the intersection of the inverse images of the mappings f and g sharing these moving hyperplanes. Our result is an improvement of many previous results in this topic.