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. Geometrical probability and random points on a hypersphere . Ann. Math. Stat ., 38 : 213 – 220 , 1967 . [3] O . Devillers , M . Glisse , X . Goaoc , G . Moroz and M . Reitzner . The monotonicity of f -vectors of random polytopes . Electron
Abstract
Relations between I-approximate Dini derivatives and monotonicity are presented. Next, some generalizations of the Denjoy–Young–Saks Theorem for I-approximate Dini derivatives of an arbitrary real function are proved.
, S. P. , Ultimate generalization to monotonicity for uniform convergence of trigonometric series , http://arxiv.org/abs/arXiv:math.CA/0611805v1 November 27, 2006, preprint. [12
. [4] Cruz-Uribe , David 1996 Piecewise monotonic doubling measures Rocky Mountain J. Math. 26 545 – 583 10.1216/rmjm/1181072073
Abstract
The Hirsch index is a number that synthesizes a researcher’s output. It is defined as the maximum number h such that the researcher has h papers with at least h citations each. Woeginger (Math Soc Sci 56: 224–232, 2008a; J Informetr 2: 298–303, 2008b) suggests two axiomatic characterizations of the Hirsch index using monotonicity as one of the axioms. This note suggests three characterizations without adopting the monotonicity axiom.
spaces Pacific J. Math. 81 371 – 377 . [8] Gao , Y. Z. , Qu , H. Z. , Wang , S. T. 2007 A note on monotonically normal spaces Acta Math. Hungar. 117 175 – 178 10.1007/s10474
References [1] Bessenyei , M. , Páles , Zs. 2010 Characterization of higher order monotonicity via integral inequalities Proc. Roy. Soc. Edinburgh Sect. A 140 723 – 736 10
. and V ural , C. , Every monotonically normal Čech-complete space is subcompact , Topology Appl. , 176 ( 2014 ), 35 – 42 . [16] T kachuk , V. V. , A C p
. , Monotonicity properties of determinants of special functions , Constr. Approx. , 26 ( 2007 ), 1 – 9 . [15] K almykov , S. I. and K arp , D. B. , Log-convexity and log
B anaś , J. and R zepka , B. , Monotonic solutions of a quadratic integral equation of fractional order , J. Math. Anal. Appl. , 332 ( 2007 ), 1371 – 1379 . 18 B
