<p>We consider the general divisor functions over Piatetski-Shapiro sequences. We present some general results on some special divisor functions. Precisely, we extend the divisor problem over Piatetski-Shapiro sequences to the functions <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\left(n\right)={\sum }_{n={n}_{1}{n}_{2}}\tau \left({n}_{1}\right)g\left({n}_{2}\right)\ll {n}^{\varepsilon },\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close=")" open="("> <mi>n</mi> </mfenced> <mo>=</mo> <msub> <mo>∑</mo> <mrow> <mi>n</mi> <mo>=</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> <msub> <mi>n</mi> <mn>2</mn> </msub> </mrow> </msub> <mi>τ</mi> <mfenced close=")" open="("> <msub> <mi>n</mi> <mn>1</mn> </msub> </mfenced> <mi>g</mi> <mfenced close=")" open="("> <msub> <mi>n</mi> <mn>2</mn> </msub> </mfenced> <mo>≪</mo> <msup> <mrow> <mi>n</mi> </mrow> <mi>ε</mi> </msup> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> , where <i>τ</i>(<i>n</i>) is the number of representations of <i>n</i> as a product of two natural numbers, and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\sum }_{1\le n\le x}\left|g\left(n\right)\right|\ll {x}^{5/8+\varepsilon }\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mo>∑</mo> <mrow> <mn>1</mn> <mo>≤</mo> <mi>n</mi> <mo>≤</mo> <mi>x</mi> </mrow> </msub> <mfenced close="|" open="|"> <mi>g</mi> <mfenced close=")" open="("> <mi>n</mi> </mfenced> </mfenced> <mo>≪</mo> <msup> <mrow> <mi>x</mi> </mrow> <mrow> <mn>5</mn> <mo stretchy="false">/</mo> <mn>8</mn> <mo>+</mo> <mi>ε</mi> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>. We also considered these arithmetic functions over Piatetski-Shapiro sequences in arithmetic progressions.</p>