Banach operator pairs, common fixed-points, invariant approximations, and ∗ -nonexpansive multimaps

Common fixed-point results are proved for II-nonexpansive maps, Ciric type maps, and ∗-nonexpansive multimaps. Invariant approximation results are obtained for these types of maps as applications. Our results extend or generalize several known results including the recent results of Chen and Li [J. Chen, Z. Li, Common fixed-points for Banach operators pairs in best approximation, J. Math. Anal. Appl. 336 (2007) 1466–1475]. In particular, we show that the results of Chen and Li on Banach operator pairs are particular cases of the results of Al-Thagafi and Shahzad [M.A. Al-Thagafi, N. Shahzad, Noncommuting selfmaps and invariant approximations, Nonlinear Anal. 64 (2006) 2778–2786].