| Summary: | The purpose of the present paper is to introduce and investigate new subclasses of analytic function class of bi-univalent functions defined in open unit disks connected with a linear q-convolution operator, which are associated with quasi-subordination. We find coefficient estimates of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfenced><mo>,</mo><mo> </mo><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow></semantics></math></inline-formula> for functions in these subclasses. Several known and new consequences of these results are also pointed out. There is symmetry between the results of the subclass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi mathvariant="script">f</mi></mrow><mrow><mi>q</mi><mo>,</mo><mrow><mo stretchy="false">∑</mo><mrow><mo> </mo></mrow></mrow></mrow><mrow><mi>μ</mi></mrow></msubsup><mo>(</mo><mi>ζ</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>ρ</mi><mo>,</mo><mi>σ</mi><mo>,</mo><mi>ϑ</mi><mo>,</mo><mi>γ</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>φ</mi><mo>)</mo></mrow></semantics></math></inline-formula> and the results of the subclass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mo>ℵ</mo></mrow><mrow><mrow><mo stretchy="false">∑</mo><mrow></mrow></mrow></mrow><mrow><mi>q</mi><mo>,</mo><mi>δ</mi></mrow></msubsup><mfenced separators="|"><mrow><mi>λ</mi><mo>,</mo><mi>ζ</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>ρ</mi><mo>,</mo><mi>σ</mi><mo>,</mo><mi>ϑ</mi><mo>,</mo><mi>φ</mi></mrow></mfenced></mrow></semantics></math></inline-formula>.
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