A ROBUST ITERATIVE APPROACH FOR SOLVING NONLINEAR VOLTERRA DELAY INTEGRO–DIFFERENTIAL EQUATIONS
This paper presents a new iterative algorithm for approximating the fixed points of multivalued generalized \(\alpha\)–nonexpansive mappings. We study the stability result of our new iterative algorithm for a larger concept of stability known as weak \(w^2\)–stability. Weak and strong convergence re...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2021-12-01
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| Series: | Ural Mathematical Journal |
| Subjects: | |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/398 |
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| Summary: | This paper presents a new iterative algorithm for approximating the fixed points of multivalued generalized \(\alpha\)–nonexpansive mappings. We study the stability result of our new iterative algorithm for a larger concept of stability known as weak \(w^2\)–stability. Weak and strong convergence results of the proposed iterative algorithm are also established. Furthermore, we show numerically that our new iterative algorithm outperforms several known iterative algorithms for multivalued generalized \(\alpha\)–nonexpansive mappings. Again, as an application, we use our proposed iterative algorithm to find the solution of nonlinear Volterra delay integro-differential equations. Finally, we provide an illustrative example to validate the mild conditions used in the result of the application part of this study. Our results improve, generalize and unify several results in the existing literature. |
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| ISSN: | 2414-3952 |