A New Class of Function with Finitely Many Fixed Points

The study introduced a generalized multiplier operator used as a tool to define and investigate a new class of function, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:mi>T</a:mi><a:mi>S</a:mi><a:msubsup><a:mrow><a:mi>Q</a:mi></a:mrow><a:mrow><a:mi>σ</a:mi><a:mo>,</a:mo><a:mi>ξ</a:mi><a:mo>,</a:mo><a:mi>ω</a:mi><a:mo>,</a:mo><a:mi>ε</a:mi></a:mrow><a:mrow><a:mi>μ</a:mi><a:mo>,</a:mo><a:mi>λ</a:mi><a:mo>,</a:mo><a:mi>η</a:mi></a:mrow></a:msubsup><a:mfenced open="(" close=")"><a:mrow><a:mi>ϖ</a:mi><a:mo>,</a:mo><a:mi>n</a:mi></a:mrow></a:mfenced></a:math> and its subclass <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M2"><e:mi>T</e:mi><e:mi>S</e:mi><e:msubsup><e:mrow><e:mi>Q</e:mi></e:mrow><e:mrow><e:mi>σ</e:mi><e:mo>,</e:mo><e:mi>ξ</e:mi><e:mo>,</e:mo><e:mi>ω</e:mi><e:mo>,</e:mo><e:mi>ε</e:mi></e:mrow><e:mrow><e:mi>μ</e:mi><e:mo>,</e:mo><e:mi>λ</e:mi><e:mo>,</e:mo><e:mi>η</e:mi></e:mrow></e:msubsup><e:mfenced open="(" close=")"><e:mrow><e:mi>ϖ</e:mi><e:mo>,</e:mo><e:mi>n</e:mi><e:mo>;</e:mo><e:msub><e:mrow><e:mi>M</e:mi></e:mrow><e:mrow><e:mi>i</e:mi></e:mrow></e:msub></e:mrow></e:mfenced></e:math> . Various properties of the class of functions were investigated. The results extend some known results in literature.