@article {ChSaSoMi2005,
 author="Yong-Gao Chen, Andr\'{a}s S\'{a}rk\"{o}zy, Vera T. S\'{o}s and Min Tang",
 title={On the monotonicity properties of additive representation functions},
 journal="Bull. Austral. Math. Soc.",
 fjournal={Bulletin of the Australian Mathematical Society},
 volume="72",
 year="2005",
 number="1",
 pages="129--138",
 issn="0004-9727",
 coden="ALNBAB",
 language="English",
 date="29th March, 2005",
 classmath="11B34",
 publisher={AMPAI, Australian Mathematical Society},
 MRnumber="MR2162298",
 ZBLnumber="02212190",
 url="http://www.austms.org.au/Publ/Bulletin/V72P1/721-5098-ChSaSoMi/index.shtml",
 acknowledgement={Research supported by the NSF of China Grant 10471064, the SF of AnHui Province Grant 01046103 and the Hungarian National Foundation for Scientific Research Grant T043623, T042750, T038210, T046378. },
 abstract={ If $A$ is a set of positive integers, let $R_{1} (n)$ be the number of solutions of $a+a' = n $, $a$, $a'\in A$, and let $R_{2}(n)$ and $R_{3}(n)$ denote the number of solutions with the additional restrictions $a<a'$, and $a\leq a'$ respectively. The monotonicity properties of the three functions $R_{1}(n)$, $R_{2}(n)$, and $R_{3}(n)$ are studied and compared. }
}