Fixed point theorems for nonlinear mappings and strict convexity of banach spaces
In this paper, we first prove a fixed point theorem for generalized nonexpansive type mappings in a Banach space by using Kohsaka and Takahashi's fixed point theorem [10] for nonspreading mappings. Then using Takahashi, Yao and Kohsaka's result [21], we obtain a necessary and sufficient co...
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| Main Authors: | , , , |
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| Format: | Journal |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=78650736801&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/51000 |
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| Institution: | Chiang Mai University |
| Summary: | In this paper, we first prove a fixed point theorem for generalized nonexpansive type mappings in a Banach space by using Kohsaka and Takahashi's fixed point theorem [10] for nonspreading mappings. Then using Takahashi, Yao and Kohsaka's result [21], we obtain a necessary and sufficient condition for the existence of fixed points of generalized nonexpansive type mappings. Further, we prove a fixed point theorem for nonspreading mappings with compact domains in a Banach space. Using this result, we give a necessary and sufficient condition for strict convexity of Banach spaces. |
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