Generalization of some retarded integral inequalities with power in two independent variables and applications
In this work, some new kinds of nonlinear power integral inequalities in two-dimensional cases are introduced. With advanced analytical mathematical methods, many estimations are obtained in order to generalize to higher order, well known results in the literature for $ p = 1 $ and $ p\in(0, 1] $. A...
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025191 |
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| author | Selma Mili Ammar Boudeliou |
| author_facet | Selma Mili Ammar Boudeliou |
| author_sort | Selma Mili |
| collection | DOAJ |
| description | In this work, some new kinds of nonlinear power integral inequalities in two-dimensional cases are introduced. With advanced analytical mathematical methods, many estimations are obtained in order to generalize to higher order, well known results in the literature for $ p = 1 $ and $ p\in(0, 1] $. As an example, we apply these results to determine the boundedness of solutions of nonlinear bidimensional Volterra type integral equations for $ p > 1 $. |
| format | Article |
| id | doaj-art-fb536981211449b3939166eaa8ea4feb |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-fb536981211449b3939166eaa8ea4feb2025-08-20T01:54:41ZengAIMS PressAIMS Mathematics2473-69882025-02-011024120413810.3934/math.2025191Generalization of some retarded integral inequalities with power in two independent variables and applicationsSelma Mili0Ammar Boudeliou1Department of Mathematics, University of Constantine 1 Brothers Mentouri, BP, 325, Ain El Bey Street, 25017, AlgeriaDepartment of Mathematics, University of Constantine 1 Brothers Mentouri, BP, 325, Ain El Bey Street, 25017, AlgeriaIn this work, some new kinds of nonlinear power integral inequalities in two-dimensional cases are introduced. With advanced analytical mathematical methods, many estimations are obtained in order to generalize to higher order, well known results in the literature for $ p = 1 $ and $ p\in(0, 1] $. As an example, we apply these results to determine the boundedness of solutions of nonlinear bidimensional Volterra type integral equations for $ p > 1 $.https://www.aimspress.com/article/doi/10.3934/math.2025191boundednessretarded integral inequalitypowervolterra integral equation |
| spellingShingle | Selma Mili Ammar Boudeliou Generalization of some retarded integral inequalities with power in two independent variables and applications AIMS Mathematics boundedness retarded integral inequality power volterra integral equation |
| title | Generalization of some retarded integral inequalities with power in two independent variables and applications |
| title_full | Generalization of some retarded integral inequalities with power in two independent variables and applications |
| title_fullStr | Generalization of some retarded integral inequalities with power in two independent variables and applications |
| title_full_unstemmed | Generalization of some retarded integral inequalities with power in two independent variables and applications |
| title_short | Generalization of some retarded integral inequalities with power in two independent variables and applications |
| title_sort | generalization of some retarded integral inequalities with power in two independent variables and applications |
| topic | boundedness retarded integral inequality power volterra integral equation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025191 |
| work_keys_str_mv | AT selmamili generalizationofsomeretardedintegralinequalitieswithpowerintwoindependentvariablesandapplications AT ammarboudeliou generalizationofsomeretardedintegralinequalitieswithpowerintwoindependentvariablesandapplications |