Abstract
In this paper, we introduce a new class of uniformly pointwise R-subweakly commuting self-mappings and prove several common fixed point theorems and best approximation results for uniformly pointwise R-subweakly commuting asymptotically I-nonexpansive mappings in normed linear spaces. We also establish some results concerning strong convergence of nearest common fixed points of asymptotically I-nonexpansive mappings in reflexive Banach spaces with a uniformly Gateaux differentiable norm. Our results unify and generalize various known results given by some authors to a more general class of noncommuting mappings.