Approximation Theorems and Fixed Point Theorems for Various Classes of 1-set-contractive Mappings in Banach Spaces |
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Authors: | Li Shan Liu |
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Institution: | (1) Department of Mathematics, Qufu Normal University, Shandong 273165, P. R. China |
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Abstract: | In this paper, we will prove that Ky Fan's Theorem (Math. Z. 112(1969), 234–240) is true for 1-set-contractive maps defined
on a bounded closed convex subset K in a Banach space with intK≠0. This class of 1-set-contractive maps includes condensing maps, nonexpansive maps, semicontractive maps, LANE maps and
others. As applications of our theorems, some fixed point theorems of non-selfmaps are proved under various well-known boundary
conditions. Our results are generalizations and improvements of the recent results obtained by many authors.
Project supported by the National Natural Science Foundation of China and Natural Science Foundation of
Shandong Province of China |
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Keywords: | Approximation theorems Fixed point theorems 1-set-contractive maps Semicontractive maps LANE maps |
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