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