Characterization and classification of sigmoid function and generalized discrete probability distributions series defined by Awolere–Oladipo derivative operator in the analytic univalent function space
UDC 517.53 The sigmoid function is a special function emulating biological neurons in terms of signal processing or sending alerts to various departments of the brain for responses. It is also good for machine learning, while the generalized discrete probability distribution series is useful for mo...
Gespeichert in:
| Datum: | 2026 |
|---|---|
| Hauptverfasser: | , , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2026
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9259 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: | |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513453680099328 |
|---|---|
| author | Awolere, Ibrahim Tunji Gbolagade, Adeniyi Musibau Ayeni, Adeniyi Oladipo, Abiodun Tinuoye Altınkaya, Şahsene Awolere, Ibrahim Tunji Gbolagade, Adeniyi Musibau Ayeni, Adeniyi Oladipo, Abiodun Tinuoye Altınkaya, Şahsene Altınkaya, Şahsene |
| author_facet | Awolere, Ibrahim Tunji Gbolagade, Adeniyi Musibau Ayeni, Adeniyi Oladipo, Abiodun Tinuoye Altınkaya, Şahsene Awolere, Ibrahim Tunji Gbolagade, Adeniyi Musibau Ayeni, Adeniyi Oladipo, Abiodun Tinuoye Altınkaya, Şahsene Altınkaya, Şahsene |
| author_sort | Awolere, Ibrahim Tunji |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T11:04:14Z |
| description | UDC 517.53
The sigmoid function is a special function emulating biological neurons in terms of signal processing or sending alerts to various departments of the brain for responses. It is also good for machine learning, while the generalized discrete probability distribution series is useful for modeling infectious diseases, genetic modeling, clinical trials, risk analysis, optimal pricing, ecological and climatic modeling, and conservation biology. We explore the convex combination and several other types of behaviors of the sigmoid function associated with the generalized discrete probability distribution series in the space of univalent function theory. This is done by introducing and studying a new derivative operator. Several coefficient inequalities and consequences of various choices of the parameters involved are discussed. Graphically, by using the Python software, various convex combinations of $K_{\phi}$ and $g_{\phi}$ are presented in terms of disease and intervention, policy and policy intervention, investment return, disease spread, infection and intervention, free market and intervention, and cost and efficiency relations. |
| doi_str_mv | 10.3842/umzh.v78i1-2.9259 |
| first_indexed | 2026-03-24T03:44:56Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9259 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:44:56Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-92592026-03-21T11:04:14Z Characterization and classification of sigmoid function and generalized discrete probability distributions series defined by Awolere–Oladipo derivative operator in the analytic univalent function space Characterization and classification of sigmoid function and generalized discrete probability distributions series defined by Awolere–Oladipo derivative operator in the analytic univalent function space Awolere, Ibrahim Tunji Gbolagade, Adeniyi Musibau Ayeni, Adeniyi Oladipo, Abiodun Tinuoye Altınkaya, Şahsene Awolere, Ibrahim Tunji Gbolagade, Adeniyi Musibau Ayeni, Adeniyi Oladipo, Abiodun Tinuoye Altınkaya, Şahsene Altınkaya, Şahsene Analytic function Generalized distribution series Python Complex Analysis UDC 517.53 The sigmoid function is a special function emulating biological neurons in terms of signal processing or sending alerts to various departments of the brain for responses. It is also good for machine learning, while the generalized discrete probability distribution series is useful for modeling infectious diseases, genetic modeling, clinical trials, risk analysis, optimal pricing, ecological and climatic modeling, and conservation biology. We explore the convex combination and several other types of behaviors of the sigmoid function associated with the generalized discrete probability distribution series in the space of univalent function theory. This is done by introducing and studying a new derivative operator. Several coefficient inequalities and consequences of various choices of the parameters involved are discussed. Graphically, by using the Python software, various convex combinations of $K_{\phi}$ and $g_{\phi}$ are presented in terms of disease and intervention, policy and policy intervention, investment return, disease spread, infection and intervention, free market and intervention, and cost and efficiency relations. УДК 517.53 Характеризація та класифікація сигмоїдної функції і узагальненого дискретного ряду ймовірнісних розподілів, визначених диференціальним оператором Аволере–Оладіпо, у просторі аналітичних однолистних функцій Сигмоїдну функцію розглянуто як спеціальну функцію, що моделює біологічні нейрони з погляду обробки сигналів і передавання імпульсів для формування відповідних реакцій у різних ділянках мозку. Вона також придатна для машинного навчання. Узагальнений дискретний ряд ймовірнісних розподілів застосовується для моделювання інфекційних захворювань, генетичних процесів і клінічних випробувань, аналізу ризиків, оптимального ціноутворення, екологічного та кліматичного моделювання, а також біології збереження. Вивчено опуклі комбінації та інші властивості сигмоїдної функції, пов'язані з узагальненим дискретним рядом ймовірнісних розподілів, у просторі теорії однолистних функцій. Для цього введено та проаналізовано новий диференціальний оператор. Наведено коефіцієнтні нерівності та обговорено наслідки різних виборів параметрів. Графічно, з використанням програмного забезпечення Python, подано різні опуклі комбінації $K_{\phi}$ і $g_{\phi}$ у контексті захворювань і втручань, політики та політичних втручань, інвестиційної дохідності, поширення хвороб, інфекцій і втручань, вільного ринку та регулювання, а також співвідношення вартості й ефективності. Institute of Mathematics, NAS of Ukraine 2026-03-02 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9259 10.3842/umzh.v78i1-2.9259 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 1-2 (2026); 80–81 Український математичний журнал; Том 78 № 1-2 (2026); 80–81 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9259/10621 Copyright (c) 2026 Ibrahim Tunji Awolere, Adeniyi Musibau Gbolagade, Adeniyi Ayeni, Abiodun Tinuoye Oladipo, Şahsene Altınkaya |
| spellingShingle | Awolere, Ibrahim Tunji Gbolagade, Adeniyi Musibau Ayeni, Adeniyi Oladipo, Abiodun Tinuoye Altınkaya, Şahsene Awolere, Ibrahim Tunji Gbolagade, Adeniyi Musibau Ayeni, Adeniyi Oladipo, Abiodun Tinuoye Altınkaya, Şahsene Altınkaya, Şahsene Characterization and classification of sigmoid function and generalized discrete probability distributions series defined by Awolere–Oladipo derivative operator in the analytic univalent function space |
| title | Characterization and classification of sigmoid function and generalized discrete probability distributions series defined by Awolere–Oladipo derivative operator in the analytic univalent function space |
| title_alt | Characterization and classification of sigmoid function and generalized discrete probability distributions series defined by Awolere–Oladipo derivative operator in the analytic univalent function space |
| title_full | Characterization and classification of sigmoid function and generalized discrete probability distributions series defined by Awolere–Oladipo derivative operator in the analytic univalent function space |
| title_fullStr | Characterization and classification of sigmoid function and generalized discrete probability distributions series defined by Awolere–Oladipo derivative operator in the analytic univalent function space |
| title_full_unstemmed | Characterization and classification of sigmoid function and generalized discrete probability distributions series defined by Awolere–Oladipo derivative operator in the analytic univalent function space |
| title_short | Characterization and classification of sigmoid function and generalized discrete probability distributions series defined by Awolere–Oladipo derivative operator in the analytic univalent function space |
| title_sort | characterization and classification of sigmoid function and generalized discrete probability distributions series defined by awolere–oladipo derivative operator in the analytic univalent function space |
| topic_facet | Analytic function Generalized distribution series Python Complex Analysis |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9259 |
| work_keys_str_mv | AT awolereibrahimtunji characterizationandclassificationofsigmoidfunctionandgeneralizeddiscreteprobabilitydistributionsseriesdefinedbyawolereoladipoderivativeoperatorintheanalyticunivalentfunctionspace AT gbolagadeadeniyimusibau characterizationandclassificationofsigmoidfunctionandgeneralizeddiscreteprobabilitydistributionsseriesdefinedbyawolereoladipoderivativeoperatorintheanalyticunivalentfunctionspace AT ayeniadeniyi characterizationandclassificationofsigmoidfunctionandgeneralizeddiscreteprobabilitydistributionsseriesdefinedbyawolereoladipoderivativeoperatorintheanalyticunivalentfunctionspace AT oladipoabioduntinuoye characterizationandclassificationofsigmoidfunctionandgeneralizeddiscreteprobabilitydistributionsseriesdefinedbyawolereoladipoderivativeoperatorintheanalyticunivalentfunctionspace AT altınkayasahsene characterizationandclassificationofsigmoidfunctionandgeneralizeddiscreteprobabilitydistributionsseriesdefinedbyawolereoladipoderivativeoperatorintheanalyticunivalentfunctionspace AT awolereibrahimtunji characterizationandclassificationofsigmoidfunctionandgeneralizeddiscreteprobabilitydistributionsseriesdefinedbyawolereoladipoderivativeoperatorintheanalyticunivalentfunctionspace AT gbolagadeadeniyimusibau characterizationandclassificationofsigmoidfunctionandgeneralizeddiscreteprobabilitydistributionsseriesdefinedbyawolereoladipoderivativeoperatorintheanalyticunivalentfunctionspace AT ayeniadeniyi characterizationandclassificationofsigmoidfunctionandgeneralizeddiscreteprobabilitydistributionsseriesdefinedbyawolereoladipoderivativeoperatorintheanalyticunivalentfunctionspace AT oladipoabioduntinuoye characterizationandclassificationofsigmoidfunctionandgeneralizeddiscreteprobabilitydistributionsseriesdefinedbyawolereoladipoderivativeoperatorintheanalyticunivalentfunctionspace AT altınkayasahsene characterizationandclassificationofsigmoidfunctionandgeneralizeddiscreteprobabilitydistributionsseriesdefinedbyawolereoladipoderivativeoperatorintheanalyticunivalentfunctionspace AT altınkayasahsene characterizationandclassificationofsigmoidfunctionandgeneralizeddiscreteprobabilitydistributionsseriesdefinedbyawolereoladipoderivativeoperatorintheanalyticunivalentfunctionspace |