Mutual proximinality of two sets in Lp(µ, X)
Journal of Mathematical and Computational Science · 2021
In this paper, we study mutual best approximation of two sets in the p –Bochner function spaces L p ( µ,X ), 1 ≤ p < ∞. We give some sufficient conditions on M and K as subsets of the Banach space X to guarantee that L p (and L p ( are mutually proximinal subsets in L p ( µ,X ). The main issue in this work is that we state and prove a distance formula for mutual best approximation between the two sets L p (and L p ( in L p ( µ,X ), for 1 ≤ p < ∞. Then we use this formula to obtain some other results related to our study.