Generalized convexity and inequalities

Article, Preprint English OPEN
Anderson, G. D.; Vamanamurthy, M. K.; Vuorinen, M.;

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
  • References (17)
    17 references, page 1 of 2

    J. Acz´el: A generalization of the notion of convex functions, Norske Vid. Selsk. Forhd., Trondhjem 19 (1947), no. 24, 87-90.

    G. D. Anderson, R. W. Barnard, K. C. Richards, M. K. Vamanamurthy, and M. Vuorinen: Inequalities for zero-balanced hypergeometric functions, Trans. Amer. Math. Soc. 347 (1995), 1713-1723.

    Vuorinen: Generalized elliptic integrals and modular equations, Pacific J. Math 192 (2000), 1-37.

    G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen: Conformal Invariants, Inequalities, and Quasiconformal Maps. Wiley, New York, 1997.

    Mu¨nchen, Math. Ann. 109 (1933), 405-413.

    Anal. Appl. 218 (1998), 256-268.

    Anal. Appl. 319 (2006), 450-459.

    Math. Anal. Appl. vol (2006) (to appear).

    M. Biernacki and J. Krzyz˙: On the monotonicity of certain functionals in the theory of analytic functions, Ann. Univ. M. Curie-Sklodowska 2 (1955), 134-145.

    P.S. Bullen: Handbook of means and their inequalities. Revised from the 1988 original [P. S. Bullen, D. S. Mitrinovi´c and P. M. Vasi´c, Means and their inequalities, Reidel, Dordrecht]. Mathematics and its Applications, 560. Kluwer Academic Publishers Group, Dordrecht, 2003.

  • Metrics
Share - Bookmark