International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 2, Pages 257-262
doi:10.1155/S0161171289000293
Fixed point theorems for compatible multi-valued and single-valued mappings
Hideaki Kaneko1
and Salvatore Sessa2
1Department of Mathematics and Statistics, Old Dominion University, Norfolk 23529, VA, USA
2Universita di Napoli, Facolta di Architettura, Instituto Mathematics, Via Monteoliveto 3, Napoli 80134, Italy
Abstract
The notion of compatibility for point-to-point mappings recently defined by Jungck is generalized to include multi-valued mappings. This idea is used to establish a fixed point theorem for a generalized contractive multi-valued mapping and a single-valued mapping.