title: Convergence theorems for generalized nonexpansive multivalued mappings in hyperbolic spaces.
abstract: In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some [Formula: see text]-convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535-540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditions. Our results are the extension and improvements of the recent well-known results announced in the current literature.
authors.affiliation: Department of Mathematics Education, Kyungnam University, Changwon, Gyeongnam 51767 Korea.
authors.forename: Jong Kyu
authors.initials: JK
authors.lastname: Kim
authors.affiliation: Department of Applied Mathematics, National Institute of Technology, Raipur, 492001 India.
authors.forename: Ramesh Prasad
authors.initials: RP
authors.lastname: Pathak
authors.affiliation: Department of Applied Mathematics, Shri Shankaracharya Group of Institutions, Junwani, Bhilai 490020 India.
authors.forename: Samir
authors.initials: S
authors.lastname: Dashputre
authors.affiliation: Department of Mathematics, Sant Guru Ghasidas, Govt. P. G. College, Kurud, Dhamtari 493663 India.
authors.forename: Shailesh Dhar
authors.initials: SD
authors.lastname: Diwan
authors.affiliation: Department of Applied Mathematics, National Institute of Technology, Raipur, 492001 India.
authors.forename: Rajlaxmi
authors.initials: R
authors.lastname: Gupta
keywords: Generalized nonexpansive multivalued mappings; Hyperbolic spaces; Iteration process; Strong and [Formula: see text]-convergence theorems