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There are over 100 recent articles in the literature dealing with first-, second- and third-order differential superordinations, containments and inequalities in the complex plane, none of which deals with systems of such topics. This article investigates systems of two second-order simultaneous differential containments, superordinations and inequalities in two analytic functions  p  and  q  defined in the unit disk. Ifandare domains in the complex plane, then a typical example of a system of differential containments isThe authors determine properties of the functions  p  and  q  satisfying a variety of such systems of differential containments, superordinations and inequalities.

Systems of simultaneous differential containments and superordinations in the complex plane