On End and Coupled Endpoints of θ-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, 215 (2012)], 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 mxm , 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.