| Summary: | The objective of the current paper is to find the necessary and sufficient conditions for Miller–Ross-type Poisson distribution series to be in the classes <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="double-struck">S</mi><mrow><mi mathvariant="script">T</mi></mrow><mo>*</mo></msubsup><mrow><mo>(</mo><mi>γ</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">K</mi><mi mathvariant="script">T</mi></msub><mrow><mo>(</mo><mi>γ</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of analytic functions with negative coefficients. Furthermore, we investigate several inclusion properties of the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="script">Y</mi><mi>σ</mi></msup><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>W</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> associated of the operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="double-struck">I</mi><mrow><mi>α</mi><mo>,</mo><mi>c</mi></mrow><mi>ε</mi></msubsup></semantics></math></inline-formula> defined by this distribution. We also take into consideration an integral operator connected to series of Miller–Ross-type Poisson distributions. Special cases of the main results are also considered.
|
|---|