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

Yongjie Piao

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 $F : X \to P_0(Y)$:$$F\Big(\sum_{i=1}^r x_i + \sum_{j=1}^s x_{r+j} \Big)\subseteq rF\Big(\frac{\sum_{i=1}^r x_i}{r}\Big)+sF\Big(\frac{\sum_{j=1}^s x_{r+j}{s}\Big),\forall x_i\in X, i=1,2,\cdots, r+s,$$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.

  • Keywords

additive selection map subadditive additive selection cone

  • 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}, 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 $F : X \to P_0(Y)$:$$F\Big(\sum_{i=1}^r x_i + \sum_{j=1}^s x_{r+j} \Big)\subseteq rF\Big(\frac{\sum_{i=1}^r x_i}{r}\Big)+sF\Big(\frac{\sum_{j=1}^s x_{r+j}{s}\Big),\forall x_i\in X, i=1,2,\cdots, r+s,$$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.}, 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 JO - Analysis in Theory and Applications VL - 3 SP - 294 EP - 300 PY - 2012 DA - 2012/10 SN - 28 DO - http://dor.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 KW - subadditive KW - additive selection KW - cone AB - 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.
Yongjie Piao. (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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