Coincidence Points of Parameterized Generalized Equations with Applications to Optimal Value Functions

The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence solutions generalized equations, implicit function fixed-point theorems, optimal value functions parametric optimization, etc. Using advanced machinery differentiation furnishes complete characterizations well-posedness properties multifunctions, we establish a general theorem ensuring parameter-dependent point with explicit error bounds for multifunctions between infinite-dimensional spaces. obtained major result yields new allows us derive efficient conditions semicontinuity continuity associated minimization problems subject constraints governed by equations.