Abstract
In this paper, first, existence of solutions for a variational inequality associated with a nonexpansive mapping in Hadamard spaces is studied. Then, the inexact proximal point algorithm for approximation of a solution of the variational inequality, which is also a fixed point of the nonexpansive mapping, is proposed. We prove the \({\Delta}\)-convergence of the generated sequence by the algorithm as well as the strong convergence of a Halpern-type regularization one to a fixed point of the nonexpansive mapping. Our motivation is to give a step toward investigation of variational inequalities in CAT(0) spaces.
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Khatibzadeh, H., Ranjbar, S. A variational inequality in complete CAT(0) spaces. J. Fixed Point Theory Appl. 17, 557–574 (2015). https://doi.org/10.1007/s11784-015-0245-0
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DOI: https://doi.org/10.1007/s11784-015-0245-0