A regularization method for solving the G-variational inequality problem and fixed-point problems in Hilbert spaces endowed with graphs
Copyright policy )A regularization method for solving the G-variational inequality problem and fixed-point problems in Hilbert spaces endowed with graphs
AbstractThis article considers and investigates a variational inequality problem and fixed-point problems in real Hilbert spaces endowed with graphs. A regularization method is proposed for solving a G-variational inequality problem and a common fixed-point problem of a finite family of G-nonexpansive mappings in the framework of Hilbert spaces endowed with graphs, which extends the work of Tiammee et al. (Fixed Point Theory Appl. 187, 2015) and Kangtunyakarn, A. (Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 112:437–448, 2018). Under certain conditions, a strong convergence theorem of the proposed method is proved. Finally, we provide numerical examples to support our main theorem. The numerical examples show that the speed of the proposed method is better than some recent existing methods in the literature.
Artificial intelligence, Fixed-Point Problems, directed graph, Mathematical analysis, \(G\)-inverse strongly monotone mapping, Fixed-point theorems, Fixed Point Theorems in Metric Spaces, G-inverse strongly monotone mapping, \(G\)-variational inequality problem, QA1-939, FOS: Mathematics, Regularization (linguistics), Variational inequality, Fixed Point Theorems, Directed graph, Equilibrium Problems, Hilbert space, Pure mathematics, G-variational inequality problem, Iterative Algorithms for Nonlinear Operators and Optimization, Fixed point, Variational inequalities, Computational Contact Mechanics and Variational Inequalities, Applied mathematics, Computer science, \(G\)-nonexpansive mapping, Computational Theory and Mathematics, Inequality, Computer Science, Physical Sciences, G-nonexpansive mapping, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., Geometry and Topology, regularization method, Mathematics, Regularization method
Artificial intelligence, Fixed-Point Problems, directed graph, Mathematical analysis, \(G\)-inverse strongly monotone mapping, Fixed-point theorems, Fixed Point Theorems in Metric Spaces, G-inverse strongly monotone mapping, \(G\)-variational inequality problem, QA1-939, FOS: Mathematics, Regularization (linguistics), Variational inequality, Fixed Point Theorems, Directed graph, Equilibrium Problems, Hilbert space, Pure mathematics, G-variational inequality problem, Iterative Algorithms for Nonlinear Operators and Optimization, Fixed point, Variational inequalities, Computational Contact Mechanics and Variational Inequalities, Applied mathematics, Computer science, \(G\)-nonexpansive mapping, Computational Theory and Mathematics, Inequality, Computer Science, Physical Sciences, G-nonexpansive mapping, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., Geometry and Topology, regularization method, Mathematics, Regularization method
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