A class of strongly close-to-convex functions
In this paper, we study a class of strongly close-to-convex functions $f(z)$ analytic in the unit disk $\mathbb{U}$ with $f(0)=0,f^{\prime }(0)=1$ satisfying for some convex function $g(z)$ the condition that \begin{equation*} \frac{zf^{\prime }(z)}{g(z)}\prec \left( \frac{1+Az}{1+Bz}\right)...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2019-05-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/38464 |
| _version_ | 1797633470697046016 |
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| author | R. K. Raina Poonam Sharma Janusz Sokol |
| author_facet | R. K. Raina Poonam Sharma Janusz Sokol |
| author_sort | R. K. Raina |
| collection | DOAJ |
| description |
In this paper, we study a class of strongly close-to-convex functions $f(z)$ analytic in the unit disk $\mathbb{U}$ with $f(0)=0,f^{\prime }(0)=1$ satisfying for some convex function $g(z)$ the condition that
\begin{equation*}
\frac{zf^{\prime }(z)}{g(z)}\prec \left( \frac{1+Az}{1+Bz}\right) ^{m}
\end{equation*}%
\begin{equation*}
\left( -1\leq A\leq 1,-1\leq B\leq 1\ \left( A\neq B\right) ,0<m\leq 1;z\in
\mathbb{U}\right) .
\end{equation*}%
We obtain for functions belonging to this class, the coefficient estimates, bounds, certain results based on an integral operator and radius of convexity. We also deduce a number of useful special cases and consequences of the various results which are presented in this paper.
|
| first_indexed | 2024-03-11T11:54:28Z |
| format | Article |
| id | doaj.art-10c43ab1b19a4069a379682cf46e7822 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T11:54:28Z |
| publishDate | 2019-05-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-10c43ab1b19a4069a379682cf46e78222023-11-08T20:07:21ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882019-05-0138610.5269/bspm.v38i6.38464A class of strongly close-to-convex functionsR. K. Raina0Poonam Sharma1Janusz Sokol2M.P. University of Agriculture and TechnologyUniversity of Lucknow Department of Mathematics & AstronomyUniversity of Rzeszów Faculty of Mathematics and Natural Sciences In this paper, we study a class of strongly close-to-convex functions $f(z)$ analytic in the unit disk $\mathbb{U}$ with $f(0)=0,f^{\prime }(0)=1$ satisfying for some convex function $g(z)$ the condition that \begin{equation*} \frac{zf^{\prime }(z)}{g(z)}\prec \left( \frac{1+Az}{1+Bz}\right) ^{m} \end{equation*}% \begin{equation*} \left( -1\leq A\leq 1,-1\leq B\leq 1\ \left( A\neq B\right) ,0<m\leq 1;z\in \mathbb{U}\right) . \end{equation*}% We obtain for functions belonging to this class, the coefficient estimates, bounds, certain results based on an integral operator and radius of convexity. We also deduce a number of useful special cases and consequences of the various results which are presented in this paper. https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/38464 |
| spellingShingle | R. K. Raina Poonam Sharma Janusz Sokol A class of strongly close-to-convex functions Boletim da Sociedade Paranaense de Matemática |
| title | A class of strongly close-to-convex functions |
| title_full | A class of strongly close-to-convex functions |
| title_fullStr | A class of strongly close-to-convex functions |
| title_full_unstemmed | A class of strongly close-to-convex functions |
| title_short | A class of strongly close-to-convex functions |
| title_sort | class of strongly close to convex functions |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/38464 |
| work_keys_str_mv | AT rkraina aclassofstronglyclosetoconvexfunctions AT poonamsharma aclassofstronglyclosetoconvexfunctions AT januszsokol aclassofstronglyclosetoconvexfunctions AT rkraina classofstronglyclosetoconvexfunctions AT poonamsharma classofstronglyclosetoconvexfunctions AT januszsokol classofstronglyclosetoconvexfunctions |