Generalized D-gap functions and error bound results for time-dependent variational-hemivariational inequalities

This paper first introduces a novel class of generalized difference gap (D-gap) functions derived from locally Lipschitz continuous functions, aiming to equivalently transform time-dependent variational-hemivariational inequalities into unconstrained optimization formulations.Based on this, we further establish that the generalized D-gap function exhibits local Lipschitz continuity and coercivity.Finally, under the conditions of coercivity and local -monotonicity, we present local and global error bound results for the generalized D-gap function, which provides critical theoretical support for the design and analysis of optimization algorithms.