Differentiable Solutions of a Functional Inequality

Abstract

In this paper, we find the form of differentiable solutions of the functional inequality

$$\psi\left({G\left({x,y}\right)}\right)\,\leqslant\,F\left({\psi\left(x\right),\chi\left(y\right)}\right),\,x,\,y\,\varepsilon\,\mathbb{R}$$

where ψ and χ are unknown functions. Solutions of the inequality

$$\psi\left({G\left({x,y}\right)}\right)\,\leqslant\,F\left({\psi\left(x\right),\psi\left(y\right)}\right),\,x,\,y\,\varepsilon\,\mathbb{R}$$

, possessing a differentiable majorant are also studied.