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Keywords = ℋ(·,·)-compression mapping

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17 pages, 313 KiB  
Article
Convergence Analysis of a Three-Step Iterative Algorithm for Generalized Set-Valued Mixed-Ordered Variational Inclusion Problem
by Praveen Agarwal, Doaa Filali, M. Akram and M. Dilshad
Symmetry 2021, 13(3), 444; https://doi.org/10.3390/sym13030444 - 9 Mar 2021
Cited by 11 | Viewed by 2186
Abstract
This manuscript aims to study a generalized, set-valued, mixed-ordered, variational inclusion problem involving H(·,·)-compression XOR-αM-non-ordinary difference mapping and relaxed cocoercive mapping in real-ordered Hilbert spaces. The resolvent operator associated with [...] Read more.
This manuscript aims to study a generalized, set-valued, mixed-ordered, variational inclusion problem involving H(·,·)-compression XOR-αM-non-ordinary difference mapping and relaxed cocoercive mapping in real-ordered Hilbert spaces. The resolvent operator associated with H(·,·)-compression XOR-αM-non-ordinary difference mapping is defined, and some of its characteristics are discussed. We prove existence and uniqueness results for the considered generalized, set-valued, mixed-ordered, variational inclusion problem. Further, we put forward a three-step iterative algorithm using a ⊕ operator, and analyze the convergence of the suggested iterative algorithm under some mild assumptions. Finally, we reconfirm the existence and convergence results by an illustrative numerical example. Full article
(This article belongs to the Special Issue Advanced Calculus in Problems with Symmetry)
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