On End and Coupled Endpoints of \theta-F-Contractive Set-Valued ‎Mappings‎

In this paper, we introduce a new concept in set-valued mappings which we have called condition (UHS). Then, adding this condition to a new type of contractive set-valued mappings, recently has been introduced by Amini-Harandi [Fixed and coupled fixed points of a new type contractive set-valued mapping in complete metric spaces, Fixed point theory and applications, ۲۱۵ (۲۰۱۲)], we prove that this mapping have a unique end point. Then, we state and prove a result about existence of coupled fixed point of this type of contractive set-valued mappings defined on M \times M, where M is a complete metric space (Recently, Amini- Harandi proved existence of coupled fixed point only for self mappings). Finally, we introduce one another new concept, which we have called condition (UHS)^*. Then, adding this condition we state and prove existence of coupled endpoint for such contractive set-valued mappings. Some examples are given to illustrate the results.‎