On End and Coupled Endpoints of $\theta$-$F$-Contractive Set-Valued Mappings
الموضوعات : مجله بین المللی ریاضیات صنعتیB. Mohammadi 1 , A. Alizadeh 2
1 - Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran.
2 - Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran.
الکلمات المفتاحية: Endpoint, Coupled fixed point, Coupled endpoint, Set-valued mappings., $theta$-$F$-Contractive,
ملخص المقالة :
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 $M \times M$, 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.
