Volume 28, Issue 3
Existence Problems of Additive Selection Maps for Another Type Subadditive Set-valued Map
10.3969/j.issn.1672-4070.2012.03.010

Anal. Theory Appl., 28 (2012), pp. 294-300

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• Abstract

In this paper, we consider the following subadditive set-valued map $F : X \to P_0(Y)$:$$F\Big(\sum_{i=1}^r x_i + \sum_{j=1}^s x_{r+j} \Big)\subseteq rF\Big(\frac{\sum_{i=1}^r x_i}{r}\Big)+sF\Big(\frac{\sum_{j=1}^s x_{r+j}{s}\Big),\forall x_i\in X, i=1,2,\cdots, r+s,$$where $r$ and $s$ are two natural numbers. And we discuss the existence and unique problemof additive selection maps for the above set-valued map.

• History

Published online: 2012-10

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