| Summary: | The purpose of this paper is to study the nonlinear distributed delay differential equations with impulses effects in the vectorial regulated Banach spaces <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="script">R</mi> <mo stretchy="false">(</mo> <mrow> <mo>[</mo> <mo>−</mo> <mi>r</mi> <mo>,</mo> <mn>0</mn> <mo>]</mo> </mrow> <mo>,</mo> <msup> <mi mathvariant="double-struck">R</mi> <mi>n</mi> </msup> <mo stretchy="false">)</mo> <mo>.</mo> </mrow> </semantics> </math> </inline-formula> The existence of the periodic solution of impulsive delay differential equations is obtained by using the Schäffer fixed point theorem in regulated space <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="script">R</mi> <mo stretchy="false">(</mo> <mrow> <mo>[</mo> <mo>−</mo> <mi>r</mi> <mo>,</mo> <mn>0</mn> <mo>]</mo> </mrow> <mo>,</mo> <msup> <mi mathvariant="double-struck">R</mi> <mi>n</mi> </msup> <mo stretchy="false">)</mo> <mo>.</mo> </mrow> </semantics> </math> </inline-formula>
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