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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

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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.

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, 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

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. [4] Cruz-Uribe , David 1996 Piecewise monotonic doubling measures Rocky Mountain J. Math. 26 545 – 583 10.1216/rmjm/1181072073

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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.

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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

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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

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. 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

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. , 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

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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

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