Existence Problems of Additive Selection Maps for Another Type Subadditive Set-Valued Map

Abstract

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