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

Abstract

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 RGfunctions. Finally, we give some examples to illustrate our main results.