New Aspects on the Solvability of a Multidimensional Functional Integral Equation with Multivalued Feedback Control
The current study demonstrates the existence of solutions to a multidimensional functional integral equation with multivalued feedback. We seek solutions for the multidimensional functional problem that is defined, continuous, and bounded on the semi-infinite interval. Our proof is based on the tech...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/7/653 |
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| author | Ahmed M. A. El-Sayed Hind H. G. Hashem Shorouk M. Al-Issa |
| author_facet | Ahmed M. A. El-Sayed Hind H. G. Hashem Shorouk M. Al-Issa |
| author_sort | Ahmed M. A. El-Sayed |
| collection | DOAJ |
| description | The current study demonstrates the existence of solutions to a multidimensional functional integral equation with multivalued feedback. We seek solutions for the multidimensional functional problem that is defined, continuous, and bounded on the semi-infinite interval. Our proof is based on the technique associated with measures of noncompactness by a given modulus of continuity in the space in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mspace width="3.33333pt"></mspace><mi>B</mi><mi>C</mi><mo>(</mo><msub><mi mathvariant="double-struck">R</mi><mo>+</mo></msub><mo>)</mo><mo>.</mo><mspace width="3.33333pt"></mspace></mrow></semantics></math></inline-formula> Also, some sufficient conditions are investigated to demonstrate the asymptotic stability of the solutions to that multidimensional functional equation. Additionally, we give an example and some particular cases to illustrate our outcomes. |
| first_indexed | 2024-03-11T01:18:37Z |
| format | Article |
| id | doaj.art-6d92ab17813748ac8284095d2620f749 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T01:18:37Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-6d92ab17813748ac8284095d2620f7492023-11-18T18:17:34ZengMDPI AGAxioms2075-16802023-06-0112765310.3390/axioms12070653New Aspects on the Solvability of a Multidimensional Functional Integral Equation with Multivalued Feedback ControlAhmed M. A. El-Sayed0Hind H. G. Hashem1Shorouk M. Al-Issa2Faculty of Science, Alexandria University, Alexandria 21544, EgyptFaculty of Science, Alexandria University, Alexandria 21544, EgyptFaculty of Arts and Sciences, Department of Mathematics, The International University of Beirut, Beirut 1107, LebanonThe current study demonstrates the existence of solutions to a multidimensional functional integral equation with multivalued feedback. We seek solutions for the multidimensional functional problem that is defined, continuous, and bounded on the semi-infinite interval. Our proof is based on the technique associated with measures of noncompactness by a given modulus of continuity in the space in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mspace width="3.33333pt"></mspace><mi>B</mi><mi>C</mi><mo>(</mo><msub><mi mathvariant="double-struck">R</mi><mo>+</mo></msub><mo>)</mo><mo>.</mo><mspace width="3.33333pt"></mspace></mrow></semantics></math></inline-formula> Also, some sufficient conditions are investigated to demonstrate the asymptotic stability of the solutions to that multidimensional functional equation. Additionally, we give an example and some particular cases to illustrate our outcomes.https://www.mdpi.com/2075-1680/12/7/653multidimensional integral equationexistence resultsmeasure of noncompactnessDarbo fixed-point theoremmultivalued feedback control |
| spellingShingle | Ahmed M. A. El-Sayed Hind H. G. Hashem Shorouk M. Al-Issa New Aspects on the Solvability of a Multidimensional Functional Integral Equation with Multivalued Feedback Control Axioms multidimensional integral equation existence results measure of noncompactness Darbo fixed-point theorem multivalued feedback control |
| title | New Aspects on the Solvability of a Multidimensional Functional Integral Equation with Multivalued Feedback Control |
| title_full | New Aspects on the Solvability of a Multidimensional Functional Integral Equation with Multivalued Feedback Control |
| title_fullStr | New Aspects on the Solvability of a Multidimensional Functional Integral Equation with Multivalued Feedback Control |
| title_full_unstemmed | New Aspects on the Solvability of a Multidimensional Functional Integral Equation with Multivalued Feedback Control |
| title_short | New Aspects on the Solvability of a Multidimensional Functional Integral Equation with Multivalued Feedback Control |
| title_sort | new aspects on the solvability of a multidimensional functional integral equation with multivalued feedback control |
| topic | multidimensional integral equation existence results measure of noncompactness Darbo fixed-point theorem multivalued feedback control |
| url | https://www.mdpi.com/2075-1680/12/7/653 |
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