Fixed points of multivalued mappings in metric spaces

Abstract

Admissibility of mappings are introduced to create conditions to minimally restrict various contractive conditions on pairs of points from a metric space in order to ensure fixed point property of the respective contractions. In the present work we define new admissibility conditions and control functions to obtain certain multivalued fixed point theorems. The corresponding single valued case is discussed. We define four weak contraction mappings of which two are multivalued and two are single valued. The results are without any assumption of continuity. There is an illustrative example.

Keywords

• Set valued analysis
• Cyclic (α
• β)-admissible mapping
• Multivalued mapping
• Fixed point
• Cyclic (α; β)-admissible mapping