Global exponential stability of general \(A\)-monotone implicit fuzzy proximal dynamical systems in Banach spaces. (English) Zbl 1393.47048
Summary: The purpose of this paper is to introduce the notion of general \(A\)-monotone operators in Banach spaces. Under some suitable conditions and using generalized proximal mapping technique, neural network technique and Gronwall’s inequality, a new class of general \(A\)-monotone implicit fuzzy proximal dynamical systems in Banach spaces are also proposed and analyzed through a recurrent neural network with a one-layer structure, and the existence of the solutions of the proximal dynamical systems is shown. Further, the global exponential stability of these dynamical systems is proved. The results presented in this paper improve and generalize the corresponding results in the literature.
MSC:
| 47S40 | Fuzzy operator theory |
| 37N40 | Dynamical systems in optimization and economics |
| 47H05 | Monotone operators and generalizations |
Keywords:
general \(A\)-monotone operator; generalized proximal mapping technique; generalized implicit fuzzy proximal dynamical system; neural network technique; existence and global exponential stabilityReferences:
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