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• W3170366972 abstract "Suppose <math xmlns=http://www.w3.org/1998/Math/MathML id=M1> <mfenced open=( close=)> <mrow> <msub> <mrow> <mi>p</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </mrow> </mfenced> </math> be sequence of positive reals. By <math xmlns=http://www.w3.org/1998/Math/MathML id=M2> <msub> <mrow> <mi mathvariant=script>H</mi> </mrow> <mrow> <mi>w</mi> </mrow> </msub> <mfenced open=( close=)> <mrow> <mfenced open=( close=)> <mrow> <msub> <mrow> <mi>p</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </mrow> </mfenced> </mrow> </mfenced> </math> , we represent the space of all formal power series <math xmlns=http://www.w3.org/1998/Math/MathML id=M3> <msubsup> <mrow> <mo>∑</mo> </mrow> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mo>∞</mo> </mrow> </msubsup> <msub> <mrow> <mi>a</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> <msup> <mrow> <mi>z</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msup> </math> equipped with <math xmlns=http://www.w3.org/1998/Math/MathML id=M4> <msubsup> <mrow> <mo>∑</mo> </mrow> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mo>∞</mo> </mrow> </msubsup> <msup> <mrow> <mfenced open=| close=|> <mrow> <mi>λ</mi> <msub> <mrow> <mi>a</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> <mo>/</mo> <mfenced open=( close=)> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfenced> </mrow> </mfenced> </mrow> <mrow> <msub> <mrow> <mi>p</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </mrow> </msup> <mo><</mo> <mo>∞</mo> </math> , for some <math xmlns=http://www.w3.org/1998/Math/MathML id=M5> <mi>λ</mi> <mo>></mo> <mn>0</mn> <mo>.</mo> </math> Various topological and geometric behavior of <math xmlns=http://www.w3.org/1998/Math/MathML id=M6> <msub> <mrow> <mi mathvariant=script>H</mi> </mrow> <mrow> <mi>w</mi> </mrow> </msub> <mfenced open=( close=)> <mrow> <mfenced open=( close=)> <mrow> <msub> <mrow> <mi>p</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </mrow> </mfenced> </mrow> </mfenced> </math> and the prequasi ideal constructs by <math xmlns=http://www.w3.org/1998/Math/MathML id=M7> <mi>s</mi> </math> -numbers and <math xmlns=http://www.w3.org/1998/Math/MathML id=M8> <msub> <mrow> <mi mathvariant=script>H</mi> </mrow> <mrow> <mi>w</mi> </mrow> </msub> <mfenced open=( close=)> <mrow> <mfenced open=( close=)> <mrow> <msub> <mrow> <mi>p</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </mrow> </mfenced> </mrow> </mfenced> </math> have been considered. The upper bounds for <math xmlns=http://www.w3.org/1998/Math/MathML id=M9> <mi>s</mi> </math> -numbers of infinite series of the weighted <math xmlns=http://www.w3.org/1998/Math/MathML id=M10> <mi>n</mi> </math> -th power forward shift operator on <math xmlns=http://www.w3.org/1998/Math/MathML id=M11> <msub> <mrow> <mi mathvariant=script>H</mi> </mrow> <mrow> <mi>w</mi> </mrow> </msub> <mfenced open=( close=)> <mrow> <mfenced open=( close=)> <mrow> <msub> <mrow> <mi>p</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </mrow> </mfenced> </mrow> </mfenced> </math> with applications to some entire functions are granted. Moreover, we investigate an extrapolation of Caristi’s fixed point theorem in <math xmlns=http://www.w3.org/1998/Math/MathML id=M12> <msub> <mrow> <mi mathvariant=script>H</mi> </mrow> <mrow> <mi>w</mi> </mrow> </msub> <mfenced open=( close=)> <mrow> <mfenced open=( close=)> <mrow> <msub> <mrow> <mi>p</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </mrow> </mfenced> </mrow> </mfenced> <mo>.</mo> </math>" @default.
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• W3170366972 date "2021-06-05" @default.
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• W3170366972 title "A Generalization of Caristi’s Fixed Point Theorem in the Variable Exponent Weighted Formal Power Series Space" @default.
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• W3170366972 doi "https://doi.org/10.1155/2021/9919420" @default.
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