An Application for Bi-Concave Functions Associated with <i>q</i>-Convolution
The aim of this paper is to introduce and investigate some new subclasses of bi-concave functions using <i>q</i>-convolution and some applications. These special cases are obtaining by making use of a <i>q</i>- derivative linear operator. For the new introduced subclasses, th...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/22/4680 |
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| author | Sheza M. El-Deeb Adriana Catas |
| author_facet | Sheza M. El-Deeb Adriana Catas |
| author_sort | Sheza M. El-Deeb |
| collection | DOAJ |
| description | The aim of this paper is to introduce and investigate some new subclasses of bi-concave functions using <i>q</i>-convolution and some applications. These special cases are obtaining by making use of a <i>q</i>- derivative linear operator. For the new introduced subclasses, the authors obtain the first two initial Taylor–Maclaurin coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>c</mi><mn>2</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>c</mi><mn>3</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> of bi-concave functions. For certain values of the parameters, the authors deduce interesting corollaries for coefficient bounds which imply special cases of the new introduced operator. Also, we develop two examples for coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>c</mi><mn>2</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>c</mi><mn>3</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> for certain functions. |
| first_indexed | 2024-03-09T16:38:18Z |
| format | Article |
| id | doaj.art-85601e8a4c9b4e538c59710cd26b3869 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:38:18Z |
| publishDate | 2023-11-01 |
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| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-85601e8a4c9b4e538c59710cd26b38692023-11-24T14:54:27ZengMDPI AGMathematics2227-73902023-11-011122468010.3390/math11224680An Application for Bi-Concave Functions Associated with <i>q</i>-ConvolutionSheza M. El-Deeb0Adriana Catas1Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Buraidah 52571, Saudi ArabiaDepartment of Mathematics and Computer Science, University of Oradea, 1 University Street, 410087 Oradea, RomaniaThe aim of this paper is to introduce and investigate some new subclasses of bi-concave functions using <i>q</i>-convolution and some applications. These special cases are obtaining by making use of a <i>q</i>- derivative linear operator. For the new introduced subclasses, the authors obtain the first two initial Taylor–Maclaurin coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>c</mi><mn>2</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>c</mi><mn>3</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> of bi-concave functions. For certain values of the parameters, the authors deduce interesting corollaries for coefficient bounds which imply special cases of the new introduced operator. Also, we develop two examples for coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>c</mi><mn>2</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>c</mi><mn>3</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> for certain functions.https://www.mdpi.com/2227-7390/11/22/4680bi-concaveconvolutionfractional derivativeq-derivativeq-analogue of poisson operator |
| spellingShingle | Sheza M. El-Deeb Adriana Catas An Application for Bi-Concave Functions Associated with <i>q</i>-Convolution Mathematics bi-concave convolution fractional derivative q-derivative q-analogue of poisson operator |
| title | An Application for Bi-Concave Functions Associated with <i>q</i>-Convolution |
| title_full | An Application for Bi-Concave Functions Associated with <i>q</i>-Convolution |
| title_fullStr | An Application for Bi-Concave Functions Associated with <i>q</i>-Convolution |
| title_full_unstemmed | An Application for Bi-Concave Functions Associated with <i>q</i>-Convolution |
| title_short | An Application for Bi-Concave Functions Associated with <i>q</i>-Convolution |
| title_sort | application for bi concave functions associated with i q i convolution |
| topic | bi-concave convolution fractional derivative q-derivative q-analogue of poisson operator |
| url | https://www.mdpi.com/2227-7390/11/22/4680 |
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