Abstract
In this paper, we give some characteristic properties of star-shaped sets which include a subset of a convex metric space. Using the characteristic properties, we discuss the existence problems of fixed points of nonexpansive type mappings on star-shaped subsets of convex metric spaces, which generalize the recent results obtained by Ding Xie-ping, Beg and Azam. Finally, we give an example which shows that our generalizations are essential.
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The Projects supported by the National Natural Science Foundation of China
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Lei, D., Xie-ping, D. Fixed points of nonexpansive mappings on star-shaped subsets of a convex metric space. Appl Math Mech 13, 135–141 (1992). https://doi.org/10.1007/BF02454236
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DOI: https://doi.org/10.1007/BF02454236