1 A Fan–KKM Approach to Vector Hemivariational-Like Inequalities with 𝜁 − 𝛯 - Monotonicity

Resumo

This study introduces a new class of vector hemivariational-like inequalities in Hausdorff topological vector spaces (HTVS) governed by 𝜁 − 𝛯-monotone operators. The Fan-KKM principle is used to establish new existence results for this extended inequality system, with suitable
assumptions made about the nonlinear mappings involved. This formulation broadens the classical theory of variational and hemivariational inequalities by include more complex and non-smooth operator behaviors. Our findings not only broaden the theoretical landscape, but also offer practical answers to non-smooth equilibrium problems in Contact Mechanics.