Difference Equations and Julia Sets of Several Functions for Degenerate <i>q</i>-Sigmoid Polynomials
In this article, we construct a new type of degenerate <i>q</i>-sigmoid (DQS) polynomial for sigmoid functions containing quantum numbers and find several difference equations related to it. We check how each point moves by iteratively synthesizing a quartic degenerate <i>q</i&g...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/11/791 |
| _version_ | 1797459258774650880 |
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| author | Jung-Yoog Kang Cheon-Seoung Ryoo |
| author_facet | Jung-Yoog Kang Cheon-Seoung Ryoo |
| author_sort | Jung-Yoog Kang |
| collection | DOAJ |
| description | In this article, we construct a new type of degenerate <i>q</i>-sigmoid (DQS) polynomial for sigmoid functions containing quantum numbers and find several difference equations related to it. We check how each point moves by iteratively synthesizing a quartic degenerate <i>q</i>-sigmoid (DQS) polynomial that appears differently depending on <i>q</i> in the space of a complex structure. We also construct Julia sets associated with quartic DQS polynomials and find their features. Based on this, we make some conjectures. |
| first_indexed | 2024-03-09T16:48:53Z |
| format | Article |
| id | doaj.art-68fb90dd47ad43ce90bb15610045c471 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T16:48:53Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-68fb90dd47ad43ce90bb15610045c4712023-11-24T14:42:59ZengMDPI AGFractal and Fractional2504-31102023-10-0171179110.3390/fractalfract7110791Difference Equations and Julia Sets of Several Functions for Degenerate <i>q</i>-Sigmoid PolynomialsJung-Yoog Kang0Cheon-Seoung Ryoo1Department of Mathematics Education, Silla University, Busan 46958, Republic of KoreaDepartment of Mathematics, Hannam University, Daejeon 34430, Republic of KoreaIn this article, we construct a new type of degenerate <i>q</i>-sigmoid (DQS) polynomial for sigmoid functions containing quantum numbers and find several difference equations related to it. We check how each point moves by iteratively synthesizing a quartic degenerate <i>q</i>-sigmoid (DQS) polynomial that appears differently depending on <i>q</i> in the space of a complex structure. We also construct Julia sets associated with quartic DQS polynomials and find their features. Based on this, we make some conjectures.https://www.mdpi.com/2504-3110/7/11/791(<i>q</i>,<i>h</i>)-derivative(<i>q</i>,<i>h</i>)-difference equationsDQS polynomialsJulia set |
| spellingShingle | Jung-Yoog Kang Cheon-Seoung Ryoo Difference Equations and Julia Sets of Several Functions for Degenerate <i>q</i>-Sigmoid Polynomials Fractal and Fractional (<i>q</i>,<i>h</i>)-derivative (<i>q</i>,<i>h</i>)-difference equations DQS polynomials Julia set |
| title | Difference Equations and Julia Sets of Several Functions for Degenerate <i>q</i>-Sigmoid Polynomials |
| title_full | Difference Equations and Julia Sets of Several Functions for Degenerate <i>q</i>-Sigmoid Polynomials |
| title_fullStr | Difference Equations and Julia Sets of Several Functions for Degenerate <i>q</i>-Sigmoid Polynomials |
| title_full_unstemmed | Difference Equations and Julia Sets of Several Functions for Degenerate <i>q</i>-Sigmoid Polynomials |
| title_short | Difference Equations and Julia Sets of Several Functions for Degenerate <i>q</i>-Sigmoid Polynomials |
| title_sort | difference equations and julia sets of several functions for degenerate i q i sigmoid polynomials |
| topic | (<i>q</i>,<i>h</i>)-derivative (<i>q</i>,<i>h</i>)-difference equations DQS polynomials Julia set |
| url | https://www.mdpi.com/2504-3110/7/11/791 |
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