Geodesic
Common solutions for a monotone variational inequality problem and an infinite family of inverse strongly monotone non-self operators
Filomat, Tome 37 (2023) no. 3, p. 957

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In this paper, we introduce regularization methods for finding a point, being not only a solution for a monotone variational inequality problem but also a common zero for an infinite family of inverse strongly monotone non-self operators of a closed convex subset in a real Hilbert space. In these methods, only a finite number of the operators is used at each iteration step. Applications to the problem of common fixed point for an infinite family of strictly pseudo-contractive non-self operators and the split feasibility and fixed point problems are considered. As a particular case, a regularization extragradient iterative method without prior knowledge of operator norms for solving the split feasibility problem (SFP) is obtained. Numerical examples are given for illustration.
DOI : 10.2298/FIL2303957B
Classification : 47H17, 47H09, 49J30
Keywords: Browder-Tikhonov regularization, fixed points, extragradient method 
Nguyen Buong. Common solutions for a monotone variational inequality problem and an infinite family of inverse strongly monotone non-self operators. Filomat, Tome 37 (2023) no. 3, p. 957 . doi: 10.2298/FIL2303957B
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