Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principle
Following the idea of T.A. Burton, of progressive contractions, presented in some examples (T.A. Burton, A note on existence and uniqueness for integral equations with sum of two operators: progressive contractions, Fixed Point Theory, 20 (2019), No. 1, 107-113) and the forward step method (I.A. R...
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| Format: | Article |
| Language: | English |
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ATNAA
2019-08-01
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| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/788789 |
| _version_ | 1797915968562790400 |
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| author | Ioan A. Rus |
| author_facet | Ioan A. Rus |
| author_sort | Ioan A. Rus |
| collection | DOAJ |
| description | Following the idea of T.A. Burton, of progressive contractions, presented in some examples (T.A. Burton, A
note on existence and uniqueness for integral equations with sum of two operators: progressive contractions,
Fixed Point Theory, 20 (2019), No. 1, 107-113) and the forward step method (I.A. Rus, Abstract models of
step method which imply the convergence of successive approximations, Fixed Point Theory, 9 (2008), No. 1,
293-307), in this paper we give some variants of contraction principle in the case of operators with Volterra
property. The basic ingredient in the theory of step by step contraction is G-contraction (I.A. Rus, Cyclic
representations and fixed points, Ann. T. Popoviciu Seminar of Functional Eq. Approxim. Convexity, 3
(2005), 171-178). The relevance of step by step contraction principle is illustrated by applications in the
theory of differential and integral equations. |
| first_indexed | 2024-04-10T12:49:45Z |
| format | Article |
| id | doaj.art-afae864a2f9545d89e67b6f46988ec1e |
| institution | Directory Open Access Journal |
| issn | 2587-2648 2587-2648 |
| language | English |
| last_indexed | 2024-04-10T12:49:45Z |
| publishDate | 2019-08-01 |
| publisher | ATNAA |
| record_format | Article |
| series | Advances in the Theory of Nonlinear Analysis and its Applications |
| spelling | doaj.art-afae864a2f9545d89e67b6f46988ec1e2023-02-15T16:13:51ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482587-26482019-08-013311112010.31197/atnaa.604962Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principleIoan A. Rus0Department of Mathematics, Babeş-Bolyai University, 1, Kogălniceanu Street, 400084, Cluj-Napoca, Romania.Following the idea of T.A. Burton, of progressive contractions, presented in some examples (T.A. Burton, A note on existence and uniqueness for integral equations with sum of two operators: progressive contractions, Fixed Point Theory, 20 (2019), No. 1, 107-113) and the forward step method (I.A. Rus, Abstract models of step method which imply the convergence of successive approximations, Fixed Point Theory, 9 (2008), No. 1, 293-307), in this paper we give some variants of contraction principle in the case of operators with Volterra property. The basic ingredient in the theory of step by step contraction is G-contraction (I.A. Rus, Cyclic representations and fixed points, Ann. T. Popoviciu Seminar of Functional Eq. Approxim. Convexity, 3 (2005), 171-178). The relevance of step by step contraction principle is illustrated by applications in the theory of differential and integral equations.https://dergipark.org.tr/en/download/article-file/788789space of continuous functionoperator with volterra propertymax-normbielecki normcontractiong-contractionfiber contractionprogressive contractionstep by step contractionfixed pointpicard operatorweakly picard operatordifferential equationintegral equationconjecture. |
| spellingShingle | Ioan A. Rus Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principle Advances in the Theory of Nonlinear Analysis and its Applications space of continuous function operator with volterra property max-norm bielecki norm contraction g-contraction fiber contraction progressive contraction step by step contraction fixed point picard operator weakly picard operator differential equation integral equation conjecture. |
| title | Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principle |
| title_full | Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principle |
| title_fullStr | Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principle |
| title_full_unstemmed | Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principle |
| title_short | Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principle |
| title_sort | some variants of contraction principle in the case of operators with volterra property step by step contraction principle |
| topic | space of continuous function operator with volterra property max-norm bielecki norm contraction g-contraction fiber contraction progressive contraction step by step contraction fixed point picard operator weakly picard operator differential equation integral equation conjecture. |
| url | https://dergipark.org.tr/en/download/article-file/788789 |
| work_keys_str_mv | AT ioanarus somevariantsofcontractionprincipleinthecaseofoperatorswithvolterrapropertystepbystepcontractionprinciple |