Simultaneous Approximations in Banach Space-Valued Bochner-Lebesgue Spaces with Variable Exponent

Let oA; A; lthorn be a r- finite positive measure space and let X be a Banach space. Denote LpothornoA; A; Xthorn the X- valued Bochner- Lebesgue spaces with variable exponent pothorn; where pothorn be a l measurable function on A and take values in 1/2 1; 1: We establish some N- simultaneous proximinality results of LpothornoA; A0; Ythorn in LpothornoA; A; Xthorn if 1< ess infy2A poythorn and ess supy2A poythorn< 1; where A0 be a sub- algebra of A and Y be a nonempty locally weakly compact convex subset of X.