Generalized Convexity and Inequalities

Article, Preprint English OPEN
Anderson, G. D.; Vamanamurthy, M. K.; Vuorinen, M.;
  • Publisher: Elsevier BV
  • Journal: Journal of Mathematical Analysis and Applications,volume 335,issue 2,pages1,294-1,308 (issn: 0022-247X)
  • Related identifiers: doi: 10.1016/j.jmaa.2007.02.016
  • Subject: Applied Mathematics | Mathematics - Classical Analysis and ODEs | 33C20 (Primary) | 26A51 (Secondary) | Analysis | 33C05

Let R+ = (0,infinity) and let M be the family of all mean values of two numbers in R+ (some examples are the arithmetic, geometric, and harmonic means). Given m1, m2 in M, we say that a function f : R+ to R+ is (m1,m2)-convex if f(m1(x,y)) < or = m2(f(x),f(y)) for all x... View more
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