| Summary: | In this paper, we introduce two new generalized core inverses, namely, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>,</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>-core inverse and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>⟨</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>,</mo><mi>n</mi><mo>⟩</mo></mrow></semantics></math></inline-formula>-core inverse; both extend the inverses of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>⟨</mo><mi mathvariant="normal">i</mi><mo>,</mo><mi mathvariant="normal">m</mi><mo>⟩</mo></mrow></semantics></math></inline-formula>-core inverse, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="normal">j</mi><mo>,</mo><mi mathvariant="normal">m</mi><mo>)</mo></mrow></semantics></math></inline-formula>-core inverse, the core inverse, the core-EP inverse and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>DMP</mi></semantics></math></inline-formula>-inverse.
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