Generalized variational inclusion: graph convergence and dynamical system approach

Doaa Filali; Mohammad Dilshad; Mohammad Akram; Doaa Filali; Mohammad Dilshad; Mohammad Akram

doi:10.3934/math.20241194

AIMS Mathematics

2024, Volume 9, Issue 9: 24525-24545. doi: 10.3934/math.20241194

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Research article Special Issues

Generalized variational inclusion: graph convergence and dynamical system approach

1.
Department of Mathematical Science, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
3.
Department of Mathematics, Islamic University of Madinah, Madinah 42351, Saudi Arabia

Received: 29 May 2024 Revised: 13 July 2024 Accepted: 25 July 2024 Published: 21 August 2024
MSC : 47H05, 47H09, 47H10, 47H22, 47H25, 49J40

This work focused on the investigation of a generalized variation inclusion problem. The resolvent operator for generalized $ \eta $-co-monotone mapping was structured, the Lipschitz constant was estimated and its relationship with the graph convergence was accomplished. An Ishikawa type iterative algorithm was designed by incorporating the resolvent operator and total asymptotically non-expansive mapping. By employing the novel implication of graph convergence and analyzing the convergence of the considered iterative method, the common solution of the generalized variational inclusion and the set of fixed points of a total asymptotically non-expansive mapping was obtained. Moreover, a generalized resolvent dynamical system was investigated. Some of its attributes were discussed and implemented to examine the considered generalized variation inclusion problem.
- $ \eta $-co-monotone mapping,
- graph convergence,
- total asymptotically non-expansive mapping,
- resolvent dynamical system,
- generalized variational inclusion
Citation: Doaa Filali, Mohammad Dilshad, Mohammad Akram. Generalized variational inclusion: graph convergence and dynamical system approach[J]. AIMS Mathematics, 2024, 9(9): 24525-24545. doi: 10.3934/math.20241194

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Abstract

This work focused on the investigation of a generalized variation inclusion problem. The resolvent operator for generalized $ \eta $-co-monotone mapping was structured, the Lipschitz constant was estimated and its relationship with the graph convergence was accomplished. An Ishikawa type iterative algorithm was designed by incorporating the resolvent operator and total asymptotically non-expansive mapping. By employing the novel implication of graph convergence and analyzing the convergence of the considered iterative method, the common solution of the generalized variational inclusion and the set of fixed points of a total asymptotically non-expansive mapping was obtained. Moreover, a generalized resolvent dynamical system was investigated. Some of its attributes were discussed and implemented to examine the considered generalized variation inclusion problem.

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