| Summary: | For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>∈</mo><msup><mi mathvariant="double-struck">N</mi><mo>*</mo></msup></mrow></semantics></math></inline-formula>, let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Σ</mo><mi>p</mi></msub></semantics></math></inline-formula> denote the class of meromorphic p-valent functions. We consider an operator for meromorphic functions denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><mi>b</mi></mrow><mi>n</mi></msubsup></semantics></math></inline-formula>, which generalizes some previously studied operators. We introduce some new subclasses of the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Σ</mo><mi>p</mi></msub></semantics></math></inline-formula>, associated with subordination using the above operator, and we prove that these classes are preserved regarding the operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>J</mi><mrow><mi>p</mi><mo>,</mo><mi>γ</mi></mrow></msub></semantics></math></inline-formula>, so we have symmetry when we look at the form of the class in which we consider the function <i>g</i> and at the form of the class of the image <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>J</mi><mrow><mi>p</mi><mo>,</mo><mi>γ</mi></mrow></msub><mrow><mo>(</mo><mi>g</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>J</mi><mrow><mi>p</mi><mo>,</mo><mi>γ</mi></mrow></msub><mrow><mo>(</mo><mi>g</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mrow><mfrac><mrow><mi>γ</mi><mo>−</mo><mi>p</mi></mrow><msup><mi>z</mi><mi>γ</mi></msup></mfrac><msubsup><mo>∫</mo><mn>0</mn><mi>z</mi></msubsup><mi>g</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msup><mi>t</mi><mrow><mi>γ</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>d</mi><mi>t</mi></mrow></mstyle></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>γ</mi><mo>∈</mo><mi mathvariant="double-struck">C</mi></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Re</mi><mspace width="0.166667em"></mspace><mi>γ</mi><mo>></mo><mi>p</mi></mrow></semantics></math></inline-formula>.
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