On bounded and subcontinuous multifunctions

Alois Andreas Lechicki

Vol. 75 (1978), No. 1, 191–197

DOI: 10.2140/pjm.1978.75.191

Abstract

In this paper we extend Kocela’s conditions of boundedness of real valued functions to the case of multifunctions. Moreover the concept of subcontinuity (introduced by R. E. Smithson) is considered with application to the following generalization of a result of Ka-Sing Lau:

Let F : X → Y be a point closed and convex multifunction taking values in a locally convex space Y and suppose F is subcontinuous. Then it is f-continuous if and only if for every functional y′∈ Y ′ the function x → sup{y′(y) : y ∈ F(x)} is continuous.

Mathematical Subject Classification 2000

Primary: 54C60

Milestones

Received: 30 November 1976

Revised: 21 April 1977

Published: 1 March 1978