<p>In this paper, we acquaint universally prestarlike generalized functions of order <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1307_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\vartheta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϑ</mi> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1307_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">$\vartheta \le 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϑ</mi> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> associated with generalized telephone numbers and we get coefficient bounds for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1307_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="81" /> </InlineMediaObject> <EquationSource Format="TEX">$ f\in \mathscr {R} _{\vartheta }^{u}(\Psi )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo>∈</mo> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mi>ϑ</mi> </mrow> <mi>u</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and also for <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1307_Article_IEq4.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="97" /> </InlineMediaObject> <EquationSource Format="TEX">$ f^{-1} \in \mathscr {R} _{\vartheta }^{u}(\Psi )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>f</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>∈</mo> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mi>ϑ</mi> </mrow> <mi>u</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> which has not been discussed earlier. Further we obtain the Fekete-Szegö functional for the class of universally prestarlike functions and applications to certain probability distribution based on convolution product for such functions.</p>

Universally prestarlike functions associated with generalized telephone numbers

期刊论文
发表日期：

2025年4月18日

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G. Murugusundaramoorthy,
H. Ö. Güney

摘要

In this paper, we acquaint universally prestarlike generalized functions of order $\vartheta $ $ϑ$ with $\vartheta \le 1$ $ϑ \leq 1$ associated with generalized telephone numbers and we get coefficient bounds for $ f\in \mathscr {R} _{\vartheta }^{u}(\Psi )$ $f \in R_{ϑ}^{u} (Ψ)$ and also for $ f^{-1} \in \mathscr {R} _{\vartheta }^{u}(\Psi )$ $f^{- 1} \in R_{ϑ}^{u} (Ψ)$ which has not been discussed earlier. Further we obtain the Fekete-Szegö functional for the class of universally prestarlike functions and applications to certain probability distribution based on convolution product for such functions.