Altman’s contractors and fixed points of multivalued mappings

K. Balakrishna Reddy and P. V. Subrahmanyam

Vol. 99 (1982), No. 1, 127–136

DOI: 10.2140/pjm.1982.99.127

Abstract

Let P_i : D ⊂ X₁ ×⋯×X_n → CL(Y _i) be multivalued mappings where X_i, Y _i are Banach spaces and CL(Y _i) is the set of all nonempty closed subsets of Y _i, i = 1,⋯,n. We prove a theorem ensuring that 𝜃_i ∈ P_i(x₁,⋯,x_n) for some (x₁,⋯,x_n) ∈ D and deduce the fixed point theorems for multivalued mappings proved earlier by Czerwik, Nadler and Reich as corollaries. Besides, generalizations for multivalued mappings of the existence theorems proved by Altman using his theory of contractors are also obtained.

Mathematical Subject Classification 2000

Primary: 47H10

Secondary: 54H25, 58C15

Milestones

Received: 3 September 1980

Published: 1 March 1982