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Let <i>f</i> be analytic in the unit disk <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">D</mi><mo>=</mo><mo>{</mo><mi>z</mi><mo>∈</mo><mi mathvariant="double-struck">C</mi><mo>:</mo><mo stretchy="false">|</mo><mi>z</mi><mo stretchy="false">|</mo><mo><</mo><mn>1</mn><mo>}</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math display="inline"><semantics><mi mathvariant="script">S</mi></semantics></math></inline-formula> be the subclass of normalized univalent functions with <inline-formula><math display="inline"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, and <inline-formula><math display="inline"><semantics><mrow><msup><mi>f</mi><mo>′</mo></msup><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow><mo>=</mo><mn>1</mn><mo>.</mo></mrow></semantics></math></inline-formula> Let <i>F</i> be the inverse function of <i>f</i>, given by <inline-formula><math display="inline"><semantics><mrow><mi>F</mi><mrow><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mrow><mo>=</mo><mi>ω</mi><mo>+</mo><msubsup><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow><mo>∞</mo></msubsup><msub><mi>A</mi><mi>n</mi></msub><msup><mi>ω</mi><mi>n</mi></msup></mrow></semantics></math></inline-formula> for some <inline-formula><math display="inline"><semantics><mrow><mrow><mo stretchy="false">|</mo><mi>ω</mi><mo stretchy="false">|</mo></mrow><mo>≤</mo><msub><mi>r</mi><mn>0</mn></msub><mrow><mo stretchy="false">(</mo><mi>f</mi><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>. Let <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="script">S</mi><mo>*</mo></msup><mo>⊂</mo><mi mathvariant="script">S</mi></mrow></semantics></math></inline-formula> be the subset of starlike functions in <inline-formula><math display="inline"><semantics><mi mathvariant="double-struck">D</mi></semantics></math></inline-formula>, and <inline-formula><math display="inline"><semantics><mi mathvariant="script">C</mi></semantics></math></inline-formula> the subset of convex functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">D</mi><mo>.</mo></mrow></semantics></math></inline-formula> We show that <inline-formula><math display="inline"><semantics><mrow><mrow><mo>−</mo><mn>1</mn><mo>≤</mo><mo stretchy="false">|</mo></mrow><msub><mi>A</mi><mn>3</mn></msub><mrow><mo stretchy="false">|</mo><mo>−</mo><mo stretchy="false">|</mo></mrow><msub><mi>A</mi><mn>2</mn></msub><mrow><mo stretchy="false">|</mo><mo>≤</mo><mn>3</mn></mrow></mrow></semantics></math></inline-formula> for <inline-formula><math display="inline"><semantics><mrow><mi>f</mi><mo>∈</mo><mi mathvariant="script">S</mi></mrow></semantics></math></inline-formula>, the upper bound being sharp, and sharp upper and lower bounds for <inline-formula><math display="inline"><semantics><mrow><mrow><mo stretchy="false">|</mo></mrow><msub><mi>A</mi><mn>3</mn></msub><mrow><mo stretchy="false">|</mo><mo>−</mo><mo stretchy="false">|</mo></mrow><msub><mi>A</mi><mn>2</mn></msub><mrow><mo stretchy="false">|</mo></mrow></mrow></semantics></math></inline-formula> for the more important subclasses of <inline-formula><math display="inline"><semantics><msup><mi mathvariant="script">S</mi><mo>*</mo></msup></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mi mathvariant="script">C</mi></semantics></math></inline-formula>, and for some related classes of Bazilevič functions.