Considerable Development of the Type Additive-Quadratic g(λ)-Functional Inequalities with 3k-Variable in (α1,α2)-Homogeneous F-Spaces

In this article, I use the direct method to study two general functional inequalities with multivariables. First, I prove that the g(λ)-function inequalities (1) and (2) are additive in (α1;α2)-homogeneous F-spaces. After that, I continue to prove that the g(λ)-function inequality (1) and (2) are quadratic in the (α1;α2)-homogeneous F-space. That is the main result in this paper.