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 |
| Published: |
ATNAA
2019-08-01
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| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/788789 |
| Summary: | 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. |
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| ISSN: | 2587-2648 2587-2648 |