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• W4284893891 abstract "In this paper, using the basic concepts of symmetric <math xmlns=http://www.w3.org/1998/Math/MathML id=M1> <mi>q</mi> </math> -calculus operator theory, we define a symmetric <math xmlns=http://www.w3.org/1998/Math/MathML id=M2> <mi>q</mi> </math> -difference operator for <math xmlns=http://www.w3.org/1998/Math/MathML id=M3> <mi>m</mi> </math> -fold symmetric functions. By considering this operator, we define a new subclass <math xmlns=http://www.w3.org/1998/Math/MathML id=M4> <msub> <mrow> <mi mathvariant=normal>ℛ</mi> </mrow> <mrow> <mi>b</mi> </mrow> </msub> <mfenced open=( close=) separators=|> <mrow> <mi>φ</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>q</mi> </mrow> </mfenced> </math> of <math xmlns=http://www.w3.org/1998/Math/MathML id=M5> <mi>m</mi> </math> -fold symmetric bi-univalent functions in open unit disk <math xmlns=http://www.w3.org/1998/Math/MathML id=M6> <mi mathvariant=script>U</mi> </math> . As in applications of Faber polynomial expansions for <math xmlns=http://www.w3.org/1998/Math/MathML id=M7> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>m</mi> </mrow> </msub> <mo>∈</mo> <msub> <mrow> <mi mathvariant=normal>ℛ</mi> </mrow> <mrow> <mi>b</mi> </mrow> </msub> <mfenced open=( close=) separators=|> <mrow> <mi>φ</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>q</mi> </mrow> </mfenced> </math> , we find general coefficient <math xmlns=http://www.w3.org/1998/Math/MathML id=M8> <mfenced open=| close=| separators=|> <mrow> <msub> <mrow> <mi>a</mi> </mrow> <mrow> <mi>m</mi> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfenced> </math> for <math xmlns=http://www.w3.org/1998/Math/MathML id=M9> <mi>n</mi> <mo>≥</mo> <mn>4</mn> </math> , Fekete–Szegő problems, and initial coefficients <math xmlns=http://www.w3.org/1998/Math/MathML id=M10> <mfenced open=| close=| separators=|> <mrow> <msub> <mrow> <mi>a</mi> </mrow> <mrow> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfenced> </math> and <math xmlns=http://www.w3.org/1998/Math/MathML id=M11> <mfenced open=| close=| separators=|> <mrow> <msub> <mrow> <mi>a</mi> </mrow> <mrow> <mn>2</mn> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfenced> </math> . Also, we construct <math xmlns=http://www.w3.org/1998/Math/MathML id=M12> <mi>q</mi> </math> -Bernardi integral operator for <math xmlns=http://www.w3.org/1998/Math/MathML id=M13> <mi>m</mi> </math> -fold symmetric functions, and with the help of this newly defined operator, we discuss some applications of our main results. For validity of our result, we have chosen to give some known special cases of our main results in the form of corollaries and remarks." @default.
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• W4284893891 date "2022-07-07" @default.
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• W4284893891 title "Applications of q-Symmetric Derivative Operator to the Subclass of Analytic and Bi-Univalent Functions Involving the Faber Polynomial Coefficients" @default.
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• W4284893891 doi "https://doi.org/10.1155/2022/4250878" @default.
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