Sharp Coefficient Problems of Functions with Bounded Turnings Subordinated by Sigmoid Function
This study deals with analytic functions with bounded turnings, defined in the disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>O</mi><mi>d</mi></msub><...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-10-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/20/3862 |
| _version_ | 1797431488061374464 |
|---|---|
| author | Muhammad Arif Safa Marwa Qin Xin Fairouz Tchier Muhammad Ayaz Sarfraz Nawaz Malik |
| author_facet | Muhammad Arif Safa Marwa Qin Xin Fairouz Tchier Muhammad Ayaz Sarfraz Nawaz Malik |
| author_sort | Muhammad Arif |
| collection | DOAJ |
| description | This study deals with analytic functions with bounded turnings, defined in the disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>O</mi><mi>d</mi></msub><mo>=</mo><mfenced separators="" open="{" close="}"><mi>z</mi><mo>:</mo><mfenced open="|" close="|"><mi>z</mi></mfenced><mo><</mo><mn>1</mn></mfenced></mrow></semantics></math></inline-formula>. These functions are subordinated by sigmoid function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfrac><mn>2</mn><mrow><mn>1</mn><mo>+</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>z</mi></mrow></msup></mrow></mfrac></semantics></math></inline-formula> and their class is denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="fraktur">BT</mi><mi mathvariant="fraktur">Sg</mi></msub></semantics></math></inline-formula>. Sharp coefficient inequalities, including the third Hankel determinant for class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="fraktur">BT</mi><mi mathvariant="fraktur">Sg</mi></msub></semantics></math></inline-formula>, were investigated here. The same was also included for the logarithmic coefficients related to functions of the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="fraktur">BT</mi><mi mathvariant="fraktur">Sg</mi></msub></semantics></math></inline-formula>. |
| first_indexed | 2024-03-09T09:45:48Z |
| format | Article |
| id | doaj.art-716560bfc5b841118d975109e63e7bc2 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T09:45:48Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-716560bfc5b841118d975109e63e7bc22023-12-02T00:37:14ZengMDPI AGMathematics2227-73902022-10-011020386210.3390/math10203862Sharp Coefficient Problems of Functions with Bounded Turnings Subordinated by Sigmoid FunctionMuhammad Arif0Safa Marwa1Qin Xin2Fairouz Tchier3Muhammad Ayaz4Sarfraz Nawaz Malik5Faculty of Physical and Numerical Sciences, Abdul Wali Khan University Mardan, Mardan 23200, PakistanFaculty of Physical and Numerical Sciences, Abdul Wali Khan University Mardan, Mardan 23200, PakistanFaculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100 Torshavn, Faroe Islands, DenmarkDepartment of Mathematics, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi ArabiaFaculty of Physical and Numerical Sciences, Abdul Wali Khan University Mardan, Mardan 23200, PakistanDepartment of Mathematics, COMSATS University Islamabad, Wah Campus, Wah Cantt 47040, PakistanThis study deals with analytic functions with bounded turnings, defined in the disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>O</mi><mi>d</mi></msub><mo>=</mo><mfenced separators="" open="{" close="}"><mi>z</mi><mo>:</mo><mfenced open="|" close="|"><mi>z</mi></mfenced><mo><</mo><mn>1</mn></mfenced></mrow></semantics></math></inline-formula>. These functions are subordinated by sigmoid function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfrac><mn>2</mn><mrow><mn>1</mn><mo>+</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>z</mi></mrow></msup></mrow></mfrac></semantics></math></inline-formula> and their class is denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="fraktur">BT</mi><mi mathvariant="fraktur">Sg</mi></msub></semantics></math></inline-formula>. Sharp coefficient inequalities, including the third Hankel determinant for class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="fraktur">BT</mi><mi mathvariant="fraktur">Sg</mi></msub></semantics></math></inline-formula>, were investigated here. The same was also included for the logarithmic coefficients related to functions of the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="fraktur">BT</mi><mi mathvariant="fraktur">Sg</mi></msub></semantics></math></inline-formula>.https://www.mdpi.com/2227-7390/10/20/3862bounded turning functionlogarithmic coefficientsHankel determinantsigmoid function |
| spellingShingle | Muhammad Arif Safa Marwa Qin Xin Fairouz Tchier Muhammad Ayaz Sarfraz Nawaz Malik Sharp Coefficient Problems of Functions with Bounded Turnings Subordinated by Sigmoid Function Mathematics bounded turning function logarithmic coefficients Hankel determinant sigmoid function |
| title | Sharp Coefficient Problems of Functions with Bounded Turnings Subordinated by Sigmoid Function |
| title_full | Sharp Coefficient Problems of Functions with Bounded Turnings Subordinated by Sigmoid Function |
| title_fullStr | Sharp Coefficient Problems of Functions with Bounded Turnings Subordinated by Sigmoid Function |
| title_full_unstemmed | Sharp Coefficient Problems of Functions with Bounded Turnings Subordinated by Sigmoid Function |
| title_short | Sharp Coefficient Problems of Functions with Bounded Turnings Subordinated by Sigmoid Function |
| title_sort | sharp coefficient problems of functions with bounded turnings subordinated by sigmoid function |
| topic | bounded turning function logarithmic coefficients Hankel determinant sigmoid function |
| url | https://www.mdpi.com/2227-7390/10/20/3862 |
| work_keys_str_mv | AT muhammadarif sharpcoefficientproblemsoffunctionswithboundedturningssubordinatedbysigmoidfunction AT safamarwa sharpcoefficientproblemsoffunctionswithboundedturningssubordinatedbysigmoidfunction AT qinxin sharpcoefficientproblemsoffunctionswithboundedturningssubordinatedbysigmoidfunction AT fairouztchier sharpcoefficientproblemsoffunctionswithboundedturningssubordinatedbysigmoidfunction AT muhammadayaz sharpcoefficientproblemsoffunctionswithboundedturningssubordinatedbysigmoidfunction AT sarfraznawazmalik sharpcoefficientproblemsoffunctionswithboundedturningssubordinatedbysigmoidfunction |