Stability of functional inequality in digital metric space

In the present article, the Hyers–Ulam stability of the following inequality is analyzed: 0.1 $\{\begin{array}{c}d(f(ı+ȷ),(f(ı)+f(ȷ)))\le d({\rho }_1((f(ı+ȷ)+f(ı-ȷ),2f(ı)))\hfill \\ \phantom{d(f(ı+ȷ),(f(ı)+f(ȷ)))\le }+d({\rho }_2(2f(\frac{ı+ȷ}{2}),(f(ı)+f(ȷ))))\hfill \end{array}$ \( \textstyle\begin{cases} d (f(\imath +\jmath ), \ (f(\imath )+ \ f(\jmath )) )\leq d (\rho _{1}((f(\imath +\jmath )+ f(\imath - \jmath ),\ 2f(\imath )) ) \\ \hphantom{ d (f(\imath +\jmath ), \ (f(\imath )+ \ f(\jmath )) )\leq}{}+ d (\rho _{2} (2f (\frac{\imath +\jmath}{2} ), \ (f(\imath )+ f(\jmath )) ) ) \end{cases} \) in the setting of digital metric space, where ${\rho }_1$ $\rho _{1}$ and ${\rho }_2$ $\rho _{2}$ are fixed nonzero complex numbers with $1>\sqrt{2}|{\rho }_1|+|{\rho }_2|$ $1>\sqrt{2}|\rho _{1}|+|\rho _{2}|$ by using fixed point and direct approach.