Abstract
Let be a σ-finite positive measure space and let X be a Banach space. Denote
the X-valued Bochner–Lebesgue spaces with variable exponent
where
be a μ measurable function on A and take values in
We establish some N-simultaneous proximinality results of
in
if
and
where
be a sub-algebra of
and Y be a nonempty locally weakly compact convex subset of X.