Endpoints of generalized $\phi$-contractive multivalued mappings of integral type

Document Type: Research articles


Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran


Recently‎, some researchers have established some results on existence of endpoints for multivalued mappings. In particular, Mohammadi and Rezapour's [Endpoints of Suzuki type quasi-contractive multifunctions, U.P.B. Sci. Bull., Series A, 2015] used the technique of $\alpha-\psi$-contractive mappings, due to Samet et al. (2012), to give some results about endpoints of Suzuki type quasi-contractive multifunctions satisfing property (BS). In this paper, we prove existence and uniqueness of endpoint for multivalued mappings satisfing the weaker conditions generalized $\phi$-contractivity of integral type and property (HS). This result generalize and improve Mohammadi and Rezapour's result. Also, we give an example to illustrate the usability of the result.


Article Title [Persian]

نقاط انتهایی نگاشت های مجموعه مقداری $phi$-انقباظی تعمیم یافته ازنوع انتگرالی

Abstract [Persian]