Vol. 75, No. 1, 1978

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ISSN: 0030-8730
On bounded and subcontinuous multifunctions

Alois Andreas Lechicki

Vol. 75 (1978), No. 1, 191–197
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
Authors
Alois Andreas Lechicki