A note on the H. Milloux and King-Lai Hiong's inequalities (Q2743130)

Under certain conditions, two fundamental inequalities are proved on the meromorphic functions: NEWLINE\[NEWLINE(i)\;T(r,f) \leq\overline N(r,f)+ (l+1) \overline N\left(r, {1\over r-\varphi_1} \right)+ \overline N\left( r,{1\over f^{(l)}- \varphi_2} \right)+ S(r,f).NEWLINE\]NEWLINE NEWLINE\[NEWLINE(i)\;T(r,f)\leq l\overline N\left( r,{1 \over f-\varphi_1} \right)+ \overline N\left(r, {1\over f^{(l)}-\varphi_2} \right)+ \overline N\left(r, {1\over f^{(l)}- \varphi_2}\right) +S(r,f).NEWLINE\]