Geodesic
An algorithmic approach for a class of set-valued variational inclusion problems
Filomat, Tome 37 (2023) no. 13, p. 4395

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DOI

The main goal of this paper is twofold. Our first objective is to prove the Lipschitz continuity of the proximal-point mapping associated with an H-accretive operator and to compute an estimate of its Lipschitz constant under some new appropriate conditions imposed on the parameter and mappings involved in it. Using the notion of proximal-point mapping, a new iterative algorithm is constructed for solving a new class of set-valued variational inclusion problems in the setting of q-uniformly smooth Banach spaces. As an application, the strong convergence of the sequences generated by our proposed iterative algorithm to a solution of our considered problem is proved. The second objective of this paper is to investigate and analyze the notion of αβ-H((., .), (., .))-mixed accretive mapping introduced and studied in [S. Gupta, S. Husain, V.N. Mishra, Variational inclusion governed by αβ-H((., .), (., .))-mixed accretive mapping, Filomat 31(20)(2017) 6529-6542]. Some comments concerning αβ-H((., .), (., .))-mixed accretive mapping and related conclusions appeared in the above-mentioned paper are also pointed out.
DOI : 10.2298/FIL2313395B
Classification : 47H05, 47H09, 47J20, 47J22, 47J25, 49J40
Keywords: Set-valued variational inclusion problem, Ĥ-accretive mapping, Proximal-point mapping, αβ-H((., .), (., .))-mixed accretive mapping, Iterative algorithm, Convergence analysis 
Javad Balooee; Jen-Chih Yao. An algorithmic approach for a class of set-valued variational inclusion problems. Filomat, Tome 37 (2023) no. 13, p. 4395 . doi: 10.2298/FIL2313395B
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     title = {An algorithmic approach for a class of set-valued variational inclusion problems},
     journal = {Filomat},
     pages = {4395 },
     year = {2023},
     volume = {37},
     number = {13},
     doi = {10.2298/FIL2313395B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2313395B/}
}
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