{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T05:49:24Z","timestamp":1782280164106,"version":"3.54.5"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper we prove new bounds for sums of convex or concave functions. Specifically, we prove that for all $A,B \\subseteq \\mathbb R$ finite sets, and for all $f,g$ convex or concave functions, we have $$|A + B|^{38}|f(A) + g(B)|^{38} \\gtrsim |A|^{49}|B|^{49}.$$\r\nThis result can be used to obtain bounds on a number of two-variable expanders of interest, as well as to the asymmetric sum-product problem. We also adjust our technique to prove the three-variable expansion result $$|AB+A|\\gtrsim |A|^{\\frac{3}{2} +\\frac{3}{170}}\\,.$$Our methods follow a series of recent developments in the sum-product literature, presenting a unified picture. Of particular interest is an adaptation of a regularisation technique of Xue, originating in a paper of Rudnev, Shakan, and Shkredov, that enables us to find positive proportion subsets with certain desirable properties.<\/jats:p>","DOI":"10.37236\/10852","type":"journal-article","created":{"date-parts":[[2022,5,6]],"date-time":"2022-05-06T08:07:04Z","timestamp":1651824424000},"source":"Crossref","is-referenced-by-count":6,"title":["On Sum Sets and Convex Functions"],"prefix":"10.37236","volume":"29","author":[{"given":"Sophie","family":"Stevens","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Audie","family":"Warren","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2022,5,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i2p18\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i2p18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,6]],"date-time":"2022-05-06T08:07:05Z","timestamp":1651824425000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i2p18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,6]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,4,8]]}},"URL":"https:\/\/doi.org\/10.37236\/10852","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,6]]},"article-number":"P2.18"}}