Banach operator pairs,common fixed-points,invariant approximations,and ∗ -nonexpansive multimaps |
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Authors: | MA Al-Thagafi Naseer Shahzad |
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Institution: | Department of Mathematics, King AbdulAziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia |
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Abstract: | Common fixed-point results are proved for I-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]. |
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Keywords: | 41A50 47H10 54H25 |
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