Geodesic
Revised algorithm for finding a common solution of variational inclusion and fixed point problems
Filomat, Tome 37 (2023) no. 20, p. 6949

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DOI

Recent research has uncovered an algorithm for locating the common solution to variational inclusion problems with multivalued maximal monotone mapping and α-inverse strongly monotone mapping, as well as the points that are invariant under non-expansive mapping. In their algorithm, Zhang et al. [S. Zhang, J. H. W. Lee, C. K. Chan, Algorithms of common solutions to quasi-variational inclusion and fixed point problems, Appl. Math. Mech. 29(5) (2008), 571–581.], λ must satisfy a very strict condition, namely λ ∈ [0, 2α]; thus, it cannot be used for all Lipschitz continuous mappings, despite the fact that inverse strongly monotone implies Lipschitz continuous. This manuscript aims to define a new algorithm that addresses the flaws of the previously described algorithm. Our algorithm is used to solve minimization problems involving the fixed point set of a non-expansive mapping. In addition, we support all of our claims with numerical examples derived from computer simulation.
DOI : 10.2298/FIL2320949Y
Classification : 47J05, 47H09, 47H10
Keywords: Variational inclusion problem, Fixed point problem, Resolvent operator, New algorithm 
Mudasir Younis; Aadil Hussain Dar; Nawab Hussain. Revised algorithm for finding a common solution of variational inclusion and fixed point problems. Filomat, Tome 37 (2023) no. 20, p. 6949 . doi: 10.2298/FIL2320949Y
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     title = {Revised algorithm for finding a common solution of variational inclusion and fixed point problems},
     journal = {Filomat},
     pages = {6949 },
     year = {2023},
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     doi = {10.2298/FIL2320949Y},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2320949Y/}
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