Discussion on “Multidimensional Coincidence Points” via Recent Publications
We show that some definitions of multidimensional coincidence points are not compatible with the mixed monotone property. Thus, some theorems reported in the recent publications (Dalal et al., 2014 and Imdad et al., 2013) have gaps. We clarify these gaps and we present a new theorem to correct the m...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/287492 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850166911330942976 |
|---|---|
| author | Saleh A. Al-Mezel Hamed H. Alsulami Erdal Karapınar Antonio-Francisco Roldán López-de-Hierro |
| author_facet | Saleh A. Al-Mezel Hamed H. Alsulami Erdal Karapınar Antonio-Francisco Roldán López-de-Hierro |
| author_sort | Saleh A. Al-Mezel |
| collection | DOAJ |
| description | We show that some definitions of multidimensional coincidence points are not compatible with the mixed monotone property. Thus, some theorems reported in the recent publications (Dalal et al., 2014 and Imdad et al., 2013) have gaps. We clarify these gaps and we present a new theorem to correct the mentioned results. Furthermore, we show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. |
| format | Article |
| id | doaj-art-e5320179e48b4c1bb3a55878657eef5e |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e5320179e48b4c1bb3a55878657eef5e2025-08-20T02:21:19ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/287492287492Discussion on “Multidimensional Coincidence Points” via Recent PublicationsSaleh A. Al-Mezel0Hamed H. Alsulami1Erdal Karapınar2Antonio-Francisco Roldán López-de-Hierro3Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi ArabiaNonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi ArabiaNonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi ArabiaUniversity of Jaén, Campus las Lagunillas s/n, 23071 Jaén, SpainWe show that some definitions of multidimensional coincidence points are not compatible with the mixed monotone property. Thus, some theorems reported in the recent publications (Dalal et al., 2014 and Imdad et al., 2013) have gaps. We clarify these gaps and we present a new theorem to correct the mentioned results. Furthermore, we show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem.http://dx.doi.org/10.1155/2014/287492 |
| spellingShingle | Saleh A. Al-Mezel Hamed H. Alsulami Erdal Karapınar Antonio-Francisco Roldán López-de-Hierro Discussion on “Multidimensional Coincidence Points” via Recent Publications Abstract and Applied Analysis |
| title | Discussion on “Multidimensional Coincidence Points” via Recent Publications |
| title_full | Discussion on “Multidimensional Coincidence Points” via Recent Publications |
| title_fullStr | Discussion on “Multidimensional Coincidence Points” via Recent Publications |
| title_full_unstemmed | Discussion on “Multidimensional Coincidence Points” via Recent Publications |
| title_short | Discussion on “Multidimensional Coincidence Points” via Recent Publications |
| title_sort | discussion on multidimensional coincidence points via recent publications |
| url | http://dx.doi.org/10.1155/2014/287492 |
| work_keys_str_mv | AT salehaalmezel discussiononmultidimensionalcoincidencepointsviarecentpublications AT hamedhalsulami discussiononmultidimensionalcoincidencepointsviarecentpublications AT erdalkarapınar discussiononmultidimensionalcoincidencepointsviarecentpublications AT antoniofranciscoroldanlopezdehierro discussiononmultidimensionalcoincidencepointsviarecentpublications |