There are many articles in the literature dealing with a first, second and third-order differential inequalities, inclusions or subordinations in the complex plane, none of which deals with systems of such topics. This article investigates systems of two second-order simultaneous differential inequalities, inclusions and subordinations in two complex functions p and q in the complex plane. A typical example of a system of differential inequalities is$$ \left\{ {\begin{array}{*{20}l} {\text{Re} [2p(z) + zp^{{\prime }} (z) + z^{2} p^{{\prime \prime }} (z) - q(z)] > 0,} \hfill \\ {\text{Re} [p(z) + 7zq^{{\prime }} (z)] > 4.} \hfill \\ \end{array} } \right. $$The authors determine properties of the functions p and q satisfying some special systems of differential inequalities, and extend their results to differential inclusions and subordinations.

中文翻译：

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复平面上同时微分不等式，包含和从属的系统

文献中有许多文章涉及复杂平面中的一阶，二阶和三阶微分不等式，包含或从属关系，但都没有涉及此类主题的系统。本文研究复平面中两个复函数p和q中两个二阶同时微分不等式，包含和从属的系统。微分不等式系统的典型示例是$$ \ left \ {{\ begin {array} {* {20} l} {\ text {Re} [2p（z）+ zp ^ {{\ prime}}}（ z）+ z ^ {2} p ^ {{\ prime \ prime}}（z）-q（z）]> 0，} \ hfill \\ {\ text {Re} [p（z）+ 7zq ^ { {\ prime}}（z）]> 4.} \ hfill \\ \ end {array}} \ right。$$作者确定函数p和q的属性 满足一些特殊的微分不等式系统，并将其结果扩展到微分包含和从属关系。