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1: 1.4 Calculus of One Variable

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§1.4(i) Monotonicity

… ►If the $\le$ sign is replaced by , then $f(x)$ is increasing (also called strictly increasing) on $I$. Similarly for nonincreasing and decreasing (strictly decreasing) functions. Each of the preceding four cases is classified as monotonic; sometimes strictly monotonic is used for the strictly increasing or strictly decreasing cases. … ►For $f(x)$ monotonic and $\varphi (x)$ integrable on $[a,b]$, there exists $c\in [a,b]$, such that …

2: 23.20 Mathematical Applications

… ►The boundary of the rectangle $R$, with vertices $0$, ${\omega }_1$, ${\omega }_1+{\omega }_3$, ${\omega }_3$, is mapped strictly monotonically by $\mathrm{\wp }$ onto the real line with $0\to \mathrm{\infty }$, ${\omega }_1\to e_1$, ${\omega }_1+{\omega }_3\to e_2$, ${\omega }_3\to e_3$, $0\to -\mathrm{\infty }$. … ►The two pairs of edges $[0,{\omega }_1]\cup [{\omega }_1,2{\omega }_3]$ and $[2{\omega }_3,2{\omega }_3-{\omega }_1]\cup [2{\omega }_3-{\omega }_1,0]$ of $R$ are each mapped strictly monotonically by $\mathrm{\wp }$ onto the real line, with $0\to \mathrm{\infty }$, ${\omega }_1\to e_1$, $2{\omega }_3\to -\mathrm{\infty }$; similarly for the other pair of edges. …

3: 10.37 Inequalities; Monotonicity

§10.37 Inequalities; Monotonicity

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4: 4.12 Generalized Logarithms and Exponentials

… ►and is strictly increasing when $0\le x\le 1$. …It, too, is strictly increasing when $0\le x\le 1$, and …

5: 10.14 Inequalities; Monotonicity

§10.14 Inequalities; Monotonicity

… ►For monotonicity properties of $J_{\nu }\left(\nu \right)$ and $J_{\nu }^{\prime }\left(\nu \right)$ see Lorch (1992). … ►For further monotonicity properties see Landau (1999, 2000), and Muldoon and Spigler (1984).

6: 35.9 Applications

… ►For other statistical applications of ${}_p{}^{}F_q^{}$ functions of matrix argument see Perlman and Olkin (1980), Groeneboom and Truax (2000), Bhaumik and Sarkar (2002), Richards (2004) (monotonicity of power functions of multivariate statistical test criteria), Bingham et al. (1992) (Procrustes analysis), and Phillips (1986) (exact distributions of statistical test criteria). …

7: Bibliography L

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Monotonicity properties of zeros of generalized Airy functions. Z. Angew. Math. Phys. 39 (2), pp. 267–271.

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External Links:

ISSN 0044-2275, Document, MathReview (Evangelos Ifantis), ZentralBlatt

Referenced by:

§9.13(i).

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Monotonicity results and inequalities for the gamma and error functions. J. Comput. Appl. Math. 23 (1), pp. 25–33.

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External Links:

ISSN 0377-0427, Document, MathReview (M. E. Cohen), ZentralBlatt

Referenced by:

§7.8.

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Bessel functions: Monotonicity and bounds. J. London Math. Soc. (2) 61 (1), pp. 197–215.

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External Links:

ISSN 0024-6107, Document, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§10.14, §10.15.

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Monotonicity and convexity properties of zeros of Bessel functions. SIAM J. Math. Anal. 8 (1), pp. 171–178.

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External Links:

ISSN 1095-7154, Document, MathReview (T. Erber), ZentralBlatt

Referenced by:

§10.21(iv).

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Higher monotonicity properties of certain Sturm-Liouville functions. III. Canad. J. Math. 22, pp. 1238–1265.

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External Links:

ISSN 0008-414X, MathReview (G. Sansone), ZentralBlatt

Referenced by:

§10.21(ii).

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8: 2.2 Transcendental Equations

… ►Let $f(x)$ be continuous and strictly increasing when and …

9: Notices

… ►Reproduction, copying, or distribution for any commercial purpose is strictly prohibited. …

10: 7.8 Inequalities

… ►The function $F\left(x\right)/\sqrt{1-{\mathrm{e}}^{-2x^2}}$ is strictly decreasing for $x>0$. …