Sixuan Bai, Rong Hu, Yi-bin Xiao, Generalized D-gap functions and error bound results for time-dependent variational-hemivariational inequalities

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DOI: 10.23952/jnva.9.2025.5.06

Volume 9, Issue 5, 1 October 2025, Pages 735-753

Abstract. 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 $\xi$ -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.

How to Cite this Article:
S. Bai, R. Hu, Y.B. Xiao, Generalized D-gap functions and error bound results for time-dependent variational-hemivariational inequalities, J. Nonlinear Var. Anal. 9 (2025), 735-753.