| Summary: | In this paper, four kinds of shadowing properties in non-autonomous discrete dynamical systems (NDDSs) are discussed. It is pointed out that if an NDDS has a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-shadowing property (resp. ergodic shadowing property, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mi>d</mi><mo>¯</mo></mover></semantics></math></inline-formula> shadowing property, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><munder><mi>d</mi><mo>̲</mo></munder></semantics></math></inline-formula> shadowing property), then the compound systems, conjugate systems, and product systems all have accordant shadowing properties. Moreover, the set-valued system <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="script">K</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>,</mo><msub><mover accent="true"><mi>f</mi><mo>¯</mo></mover><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo>)</mo></mrow></semantics></math></inline-formula> induced by the NDDS <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>X</mi><mo>,</mo><msub><mi>f</mi><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo>)</mo></mrow></semantics></math></inline-formula> has the above four shadowing properties, implying that the NDDS <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>X</mi><mo>,</mo><msub><mi>f</mi><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo>)</mo></mrow></semantics></math></inline-formula> has these properties.
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