Fixed Point of Multifunctions on Cone Metric Spaces

Abstract

On a vector space, one can define an order by using a cone in the vector space. In this way, Huang and Zhang reviewed cone metric spaces as a generalization of metric spaces with a different view (J. Math. Anal. Appl. 2007; 332:1468–1476). Most known cones are normal with normal constant M = 1. In this paper, we shall give some results about fixed point of multifunctions on the cone metric spaces with normal constant M = 1. In this way, we shall provide a generalization for main results of Kunze et al. (J. Math. Anal. Appl. 2007; 330:159–173).

Keywords:

• Cone metric space
• Cone topology
• Fixed point
• Multifunction

AMS Subject Classification:

• 47H10
• 47H04