Volume 28, Issue 3
Existence Problems of Additive Selection Maps for Another Type Subadditive Set-Valued Map

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

Published online: 2012-10

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• 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.

• AMS Subject Headings

54C65, 54C60, 39B52, 47H04, 49J54

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COPYRIGHT: © Global Science Press

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@Article{ATA-28-294, author = {Yongjie Piao , and Jin , Hailan}, title = {Existence Problems of Additive Selection Maps for Another Type Subadditive Set-Valued Map}, journal = {Analysis in Theory and Applications}, year = {2012}, volume = {28}, number = {3}, pages = {294--300}, 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.

}, issn = {1573-8175}, doi = {https://doi.org/10.3969/j.issn.1672-4070.2012.03.010}, url = {http://global-sci.org/intro/article_detail/ata/4565.html} }
TY - JOUR T1 - Existence Problems of Additive Selection Maps for Another Type Subadditive Set-Valued Map AU - Yongjie Piao , AU - Jin , Hailan JO - Analysis in Theory and Applications VL - 3 SP - 294 EP - 300 PY - 2012 DA - 2012/10 SN - 28 DO - http://doi.org/10.3969/j.issn.1672-4070.2012.03.010 UR - https://global-sci.org/intro/article_detail/ata/4565.html KW - additive selection map, subadditive, additive selection, cone. AB -

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.

Yongjie Piao & Hailan Jin. (1970). Existence Problems of Additive Selection Maps for Another Type Subadditive Set-Valued Map. Analysis in Theory and Applications. 28 (3). 294-300. doi:10.3969/j.issn.1672-4070.2012.03.010
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