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

Abstract

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.