A solution of a nonlinear Volterra integral equation with delay via a faster iteration method
The purpose of this article is to study the convergence, stability and data dependence results of an iterative method for contractive-like mappings. The concept of stability considered in this study is known as $ w^2 $-stability, which is larger than the simple notion of stability considered by seve...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-01-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023005?viewType=HTML |
| _version_ | 1797995797317419008 |
|---|---|
| author | Godwin Amechi Okeke Austine Efut Ofem Thabet Abdeljawad Manar A. Alqudah Aziz Khan |
| author_facet | Godwin Amechi Okeke Austine Efut Ofem Thabet Abdeljawad Manar A. Alqudah Aziz Khan |
| author_sort | Godwin Amechi Okeke |
| collection | DOAJ |
| description | The purpose of this article is to study the convergence, stability and data dependence results of an iterative method for contractive-like mappings. The concept of stability considered in this study is known as $ w^2 $-stability, which is larger than the simple notion of stability considered by several prominent authors. Some illustrative examples on $ w^2 $-stability of the iterative method have been presented for different choices of parameters and initial guesses. As an application of our results, we establish the existence, uniqueness and approximation results for solutions of a nonlinear Volterra integral equation with delay. Finally, we provide an illustrative example to support the application of our results. The novel results of this article extend and generalize several well known results in existing literature. |
| first_indexed | 2024-04-11T10:07:36Z |
| format | Article |
| id | doaj.art-9d7b53de40f549c1b09a6c9bd10cf1e3 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-11T10:07:36Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-9d7b53de40f549c1b09a6c9bd10cf1e32022-12-22T04:30:11ZengAIMS PressAIMS Mathematics2473-69882023-01-018110212410.3934/math.2023005A solution of a nonlinear Volterra integral equation with delay via a faster iteration methodGodwin Amechi Okeke0Austine Efut Ofem1Thabet Abdeljawad 2Manar A. Alqudah3Aziz Khan41. Department of Mathematics, College of Science and Technology, Covenant University, Canaanland, KM 10, Idiroko Road, Ota, Ogun State, Nigeria 2. Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526 Owerri, Imo State, Nigeria3. Department of Mathematics, University of Uyo, Uyo, Nigeria 4. Department of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa5. Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia 6. Department of Medical Research, China Medical University, Taichung 40402, Taiwan7. Department of Mathematical Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia5. Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaThe purpose of this article is to study the convergence, stability and data dependence results of an iterative method for contractive-like mappings. The concept of stability considered in this study is known as $ w^2 $-stability, which is larger than the simple notion of stability considered by several prominent authors. Some illustrative examples on $ w^2 $-stability of the iterative method have been presented for different choices of parameters and initial guesses. As an application of our results, we establish the existence, uniqueness and approximation results for solutions of a nonlinear Volterra integral equation with delay. Finally, we provide an illustrative example to support the application of our results. The novel results of this article extend and generalize several well known results in existing literature. https://www.aimspress.com/article/doi/10.3934/math.2023005?viewType=HTMLbanach spacedata dependence$ w^2 $-stabilitycontractive-like mappingnonlinear volterra integral equationfixed point |
| spellingShingle | Godwin Amechi Okeke Austine Efut Ofem Thabet Abdeljawad Manar A. Alqudah Aziz Khan A solution of a nonlinear Volterra integral equation with delay via a faster iteration method AIMS Mathematics banach space data dependence $ w^2 $-stability contractive-like mapping nonlinear volterra integral equation fixed point |
| title | A solution of a nonlinear Volterra integral equation with delay via a faster iteration method |
| title_full | A solution of a nonlinear Volterra integral equation with delay via a faster iteration method |
| title_fullStr | A solution of a nonlinear Volterra integral equation with delay via a faster iteration method |
| title_full_unstemmed | A solution of a nonlinear Volterra integral equation with delay via a faster iteration method |
| title_short | A solution of a nonlinear Volterra integral equation with delay via a faster iteration method |
| title_sort | solution of a nonlinear volterra integral equation with delay via a faster iteration method |
| topic | banach space data dependence $ w^2 $-stability contractive-like mapping nonlinear volterra integral equation fixed point |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023005?viewType=HTML |
| work_keys_str_mv | AT godwinamechiokeke asolutionofanonlinearvolterraintegralequationwithdelayviaafasteriterationmethod AT austineefutofem asolutionofanonlinearvolterraintegralequationwithdelayviaafasteriterationmethod AT thabetabdeljawad asolutionofanonlinearvolterraintegralequationwithdelayviaafasteriterationmethod AT manaraalqudah asolutionofanonlinearvolterraintegralequationwithdelayviaafasteriterationmethod AT azizkhan asolutionofanonlinearvolterraintegralequationwithdelayviaafasteriterationmethod AT godwinamechiokeke solutionofanonlinearvolterraintegralequationwithdelayviaafasteriterationmethod AT austineefutofem solutionofanonlinearvolterraintegralequationwithdelayviaafasteriterationmethod AT thabetabdeljawad solutionofanonlinearvolterraintegralequationwithdelayviaafasteriterationmethod AT manaraalqudah solutionofanonlinearvolterraintegralequationwithdelayviaafasteriterationmethod AT azizkhan solutionofanonlinearvolterraintegralequationwithdelayviaafasteriterationmethod |