Equations fonctionnelles et estimations de normes de matrices.
Existence criteria for positive solutions of a nonlinear difference inequality
This paper is concerned with a class of nonlinear difference inequalities which include many different classes of difference inequalities and equations as special cases. By means of a Riccati type transformation, necessary and sufficient conditions for the existence of eventually positive solutions and positive nonincreasing solutions are obtained. Various type of comparison theorems are also derived as applications, which extends many theorems in the literature.
Extensions of Popoviciu's inequality using a general method.