Geodesic
Algorithmic and analytical approach of solutions of a system of generalized multi-valued nonlinear variational inclusions
Filomat, Tome 36 (2022) no. 19, p. 6591

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The main contributions of this paper is twofold. First, our primary concern is to suggest a new iterative algorithm using the P-η-proximal-point mapping technique and Nadler's technique for finding the approximate solutions of a system of generalized multi-valued nonlinear variational-like inclusions. Under some appropriate conditions imposed on the parameters and mappings involved in the system of generalized multi-valued nonlinear variational-like inclusions, the strong convergence of the sequences generated by our proposed iterative algorithm to a solution of the aforesaid system is proved. Second, the H(., .)-η-cocoercive mapping considered in [R. Ahmad, M. Dilshad, M. Akram, Resolvent operator technique for solving a system of generalized variational-like inclusions in Banach sapces, Filomat 26(5)(2012) 897– 908] is investigated and analyzed, and the fact that under the assumptions imposed on H(., .)-η-cocoercive mapping, every H(., .)-η-cocoercive mapping is P-η-accretive and is not a new one is pointed out. At the same time, some important comments on H(., .)-η-cocoercive mapping and the results given in the above-mentioned paper are stated.
DOI : 10.2298/FIL2219591B
Classification : 47H05, 47H06, 47H09, 47J22, 47J25, 49J40, 47J20, 46C50
Keywords: Generalized multi-valued nonlinear variational inclusions, P-η-accretive mapping, H(., .)-η-cocoercive mapping, Iterative algorithm, P-η-proximal-point mapping, Convergence analysis 
Javad Balooee; Jen-Chih Yao. Algorithmic and analytical approach of solutions of a system of generalized multi-valued nonlinear variational inclusions. Filomat, Tome 36 (2022) no. 19, p. 6591 . doi: 10.2298/FIL2219591B
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     author = {Javad Balooee and Jen-Chih Yao},
     title = {Algorithmic and analytical approach of solutions of a system of generalized multi-valued nonlinear variational inclusions},
     journal = {Filomat},
     pages = {6591 },
     year = {2022},
     volume = {36},
     number = {19},
     doi = {10.2298/FIL2219591B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2219591B/}
}
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