This study uses a q-derivative operator and q-Bernoulli numbers to establish the subclass <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${\mathcal {S}}\mathfrak {B}_{q,\lambda }^{s,b}\left( \mathcal {F}_{0}\right) $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">S</mi> <msubsup> <mi mathvariant="fraktur">B</mi> <mrow> <mi>q</mi> <mo>,</mo> <mi>λ</mi> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>b</mi> </mrow> </msubsup> <mfenced close=")" open="("> <msub> <mi mathvariant="script">F</mi> <mn>0</mn> </msub> </mfenced> </mrow> </math></EquationSource> </InlineEquation> of Sakaguchi type functions. We obtained constraints for the initial coefficients <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\vert a_2 \vert $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">|</mo> </mrow> <msub> <mi>a</mi> <mn>2</mn> </msub> <mrow> <mo stretchy="false">|</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\vert a_3 \vert $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">|</mo> </mrow> <msub> <mi>a</mi> <mn>3</mn> </msub> <mrow> <mo stretchy="false">|</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> through our analysis, providing insight into the characteristics and behavior of functions in this subclass. Furthermore, we derive the Fekete-Szegö inequality that is peculiar to this class, along with a number of corollaries that expand on our results and enhance our comprehension of their implications.

Sakaguchi type functions defined by q-Bernoulli numbers

期刊论文
发表日期：

2026年2月26日

查看全文

S. Bulut,
G. Saravanan,
S. Baskaran

摘要

This study uses a q-derivative operator and q-Bernoulli numbers to establish the subclass ${\mathcal {S}}\mathfrak {B}_{q,\lambda }^{s,b}\left( \mathcal {F}_{0}\right) $ $S B_{q, λ}^{s, b} (F_{0})$ of Sakaguchi type functions. We obtained constraints for the initial coefficients $\vert a_2 \vert $ $| a_{2} |$ and $\vert a_3 \vert $ $| a_{3} |$ through our analysis, providing insight into the characteristics and behavior of functions in this subclass. Furthermore, we derive the Fekete-Szegö inequality that is peculiar to this class, along with a number of corollaries that expand on our results and enhance our comprehension of their implications.