Best approximation and fixed-point theorems for discontinuous increasing maps in Banach lattices
In this paper, we extend and prove Ky Fan’s Theorem for discontinuous increasing maps f in a Banach lattice X when f has no compact conditions. The main tools of analysis are the variational characterization of the generalized projection operator and order-theoretic fixed-point theory. Moreover, we...
| Main Authors: | , , |
|---|---|
| Format: | Journal Article |
| Published: |
SpringerOpen
2014
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/26654 |
| _version_ | 1848752047819587584 |
|---|---|
| author | Kong, D. Liu, L. Wu, Yong Hong |
| author_facet | Kong, D. Liu, L. Wu, Yong Hong |
| author_sort | Kong, D. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we extend and prove Ky Fan’s Theorem for discontinuous increasing maps f in a Banach lattice X when f has no compact conditions. The main tools of analysis are the variational characterization of the generalized projection operator and order-theoretic fixed-point theory. Moreover, we establish a sequence {xn} which converges strongly to the unique best approximation point. As an application of our best approximation theorems, a fixed-point theorem for non-self maps is established and proved under some conditions. Our results generalize and improve many recent results obtained by many authors. |
| first_indexed | 2025-11-14T08:02:25Z |
| format | Journal Article |
| id | curtin-20.500.11937-26654 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:02:25Z |
| publishDate | 2014 |
| publisher | SpringerOpen |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-266542017-09-13T15:29:11Z Best approximation and fixed-point theorems for discontinuous increasing maps in Banach lattices Kong, D. Liu, L. Wu, Yong Hong discontinuous increasing map Banach lattice generalized projection operator best approximation theorem In this paper, we extend and prove Ky Fan’s Theorem for discontinuous increasing maps f in a Banach lattice X when f has no compact conditions. The main tools of analysis are the variational characterization of the generalized projection operator and order-theoretic fixed-point theory. Moreover, we establish a sequence {xn} which converges strongly to the unique best approximation point. As an application of our best approximation theorems, a fixed-point theorem for non-self maps is established and proved under some conditions. Our results generalize and improve many recent results obtained by many authors. 2014 Journal Article http://hdl.handle.net/20.500.11937/26654 10.1186/1687-1812-2014-18 SpringerOpen fulltext |
| spellingShingle | discontinuous increasing map Banach lattice generalized projection operator best approximation theorem Kong, D. Liu, L. Wu, Yong Hong Best approximation and fixed-point theorems for discontinuous increasing maps in Banach lattices |
| title | Best approximation and fixed-point theorems for discontinuous increasing maps in Banach lattices |
| title_full | Best approximation and fixed-point theorems for discontinuous increasing maps in Banach lattices |
| title_fullStr | Best approximation and fixed-point theorems for discontinuous increasing maps in Banach lattices |
| title_full_unstemmed | Best approximation and fixed-point theorems for discontinuous increasing maps in Banach lattices |
| title_short | Best approximation and fixed-point theorems for discontinuous increasing maps in Banach lattices |
| title_sort | best approximation and fixed-point theorems for discontinuous increasing maps in banach lattices |
| topic | discontinuous increasing map Banach lattice generalized projection operator best approximation theorem |
| url | http://hdl.handle.net/20.500.11937/26654 |