An upper bound estimate for a class of split variational-hemivariational-like inequalities on Hadamard manifolds

In this paper, we introduce a class of split variational-hemivariational-like inequalities (for short, SVHLI) in the setting of Hadamard manifolds. Then a new regularized gap function (for short, RG-function) for the problem SVHLI is established under suitable assumptions. Furthermore, using the properties of strongly monotone, strong nonexpanding and skew-symmetric mappings and the generalized subdifferentials in the sense of Clarke, we provide an upper bound for the problem SVHLI in terms of RG-functions. Finally, we give some examples to illustrate our main results.