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.