Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral Equations
In this paper, we have established and proved fixed point theorems for the Boyd-Wong-type contraction in metric spaces. In particular, we have generalized the existing results for a pair of mappings that possess a fixed point but not continuous at the fixed point. We can apply this result for both c...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/9982217 |
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| author | Santosh Kumar |
| author_facet | Santosh Kumar |
| author_sort | Santosh Kumar |
| collection | DOAJ |
| description | In this paper, we have established and proved fixed point theorems for the Boyd-Wong-type contraction in metric spaces. In particular, we have generalized the existing results for a pair of mappings that possess a fixed point but not continuous at the fixed point. We can apply this result for both continuous and discontinuous mappings. We have concluded our results by providing an illustrative example for each case and an application to the existence and uniqueness of a solution of nonlinear Volterra integral equations. |
| format | Article |
| id | doaj-art-06cd24bf992f411fb3d31cf5031cbc8c |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-06cd24bf992f411fb3d31cf5031cbc8c2025-08-20T03:55:24ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/99822179982217Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral EquationsSantosh Kumar0Department of Mathematics, College of Natural and Applied Sciences, University of Dar Es Salaam, TanzaniaIn this paper, we have established and proved fixed point theorems for the Boyd-Wong-type contraction in metric spaces. In particular, we have generalized the existing results for a pair of mappings that possess a fixed point but not continuous at the fixed point. We can apply this result for both continuous and discontinuous mappings. We have concluded our results by providing an illustrative example for each case and an application to the existence and uniqueness of a solution of nonlinear Volterra integral equations.http://dx.doi.org/10.1155/2021/9982217 |
| spellingShingle | Santosh Kumar Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral Equations Journal of Function Spaces |
| title | Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral Equations |
| title_full | Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral Equations |
| title_fullStr | Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral Equations |
| title_full_unstemmed | Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral Equations |
| title_short | Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral Equations |
| title_sort | fixed points and continuity for a pair of contractive maps with application to nonlinear volterra integral equations |
| url | http://dx.doi.org/10.1155/2021/9982217 |
| work_keys_str_mv | AT santoshkumar fixedpointsandcontinuityforapairofcontractivemapswithapplicationtononlinearvolterraintegralequations |