Symmetric Functional Set-Valued Integral Equations and Bihari–LaSalle Inequality
In the paper, we consider functional set-valued integral equations whose representation contains set-valued integrals occurring symmetrically on both sides of the equation. On the coefficients of the equation, we impose certain conditions, more general than the standard Lipschitz condition, which al...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-10-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/11/2246 |
| _version_ | 1797466376551530496 |
|---|---|
| author | Marek T. Malinowski |
| author_facet | Marek T. Malinowski |
| author_sort | Marek T. Malinowski |
| collection | DOAJ |
| description | In the paper, we consider functional set-valued integral equations whose representation contains set-valued integrals occurring symmetrically on both sides of the equation. On the coefficients of the equation, we impose certain conditions, more general than the standard Lipschitz condition, which allow the application of the Bihari–LaSalle inequality in the proofs of the obtained theorems. In this way, we obtain a result about the existence and uniqueness of the solution of the equation under consideration and the insensitivity of the solution in the case of minor changes in the parameters of the equation. |
| first_indexed | 2024-03-09T18:36:04Z |
| format | Article |
| id | doaj.art-4c86e6fef89c4a02b4963d9d6d6d9b48 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T18:36:04Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-4c86e6fef89c4a02b4963d9d6d6d9b482023-11-24T07:07:13ZengMDPI AGSymmetry2073-89942022-10-011411224610.3390/sym14112246Symmetric Functional Set-Valued Integral Equations and Bihari–LaSalle InequalityMarek T. Malinowski0Department of Applied Mathematics, Tadeusz Kościuszko Cracow University of Technology, 31-155 Cracow, PolandIn the paper, we consider functional set-valued integral equations whose representation contains set-valued integrals occurring symmetrically on both sides of the equation. On the coefficients of the equation, we impose certain conditions, more general than the standard Lipschitz condition, which allow the application of the Bihari–LaSalle inequality in the proofs of the obtained theorems. In this way, we obtain a result about the existence and uniqueness of the solution of the equation under consideration and the insensitivity of the solution in the case of minor changes in the parameters of the equation.https://www.mdpi.com/2073-8994/14/11/2246set-valued integral equationsexistence and uniqueness of solutionBihari–LaSalle inequality |
| spellingShingle | Marek T. Malinowski Symmetric Functional Set-Valued Integral Equations and Bihari–LaSalle Inequality Symmetry set-valued integral equations existence and uniqueness of solution Bihari–LaSalle inequality |
| title | Symmetric Functional Set-Valued Integral Equations and Bihari–LaSalle Inequality |
| title_full | Symmetric Functional Set-Valued Integral Equations and Bihari–LaSalle Inequality |
| title_fullStr | Symmetric Functional Set-Valued Integral Equations and Bihari–LaSalle Inequality |
| title_full_unstemmed | Symmetric Functional Set-Valued Integral Equations and Bihari–LaSalle Inequality |
| title_short | Symmetric Functional Set-Valued Integral Equations and Bihari–LaSalle Inequality |
| title_sort | symmetric functional set valued integral equations and bihari lasalle inequality |
| topic | set-valued integral equations existence and uniqueness of solution Bihari–LaSalle inequality |
| url | https://www.mdpi.com/2073-8994/14/11/2246 |
| work_keys_str_mv | AT marektmalinowski symmetricfunctionalsetvaluedintegralequationsandbiharilasalleinequality |