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Search: All articles in the CMB digital archive with keyword modulus

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1. CMB 2010 (vol 54 pp. 538)

Srinivasan, Gopala Krishna; Zvengrowski, P.
On the Horizontal Monotonicity of $|\Gamma(s)|$
Writing $s = \sigma + it$ for a complex variable, it is proved that the modulus of the gamma function, $|\Gamma(s)|$, is strictly monotone increasing with respect to $\sigma$ whenever $|t| > 5/4$. It is also shown that this result is false for $|t| \leq 1$.

Keywords:Gamma function, modulus, monotonicity
Category:33B15

2. CMB 2007 (vol 50 pp. 434)

Õzarslan, M. Ali; Duman, Oktay
MKZ Type Operators Providing a Better Estimation on $[1/2,1)$
In the present paper, we introduce a modification of the Meyer-K\"{o}nig and Zeller (MKZ) operators which preserve the test functions $f_{0}(x)=1$ and $f_{2}(x)=x^{2}$, and we show that this modification provides a better estimation than the classical MKZ operators on the interval $[\frac{1}{2},1)$ with respect to the modulus of continuity and the Lipschitz class functionals. Furthermore, we present the $r-$th order generalization of our operators and study their approximation properties.

Keywords:Meyer-König and Zeller operators, Korovkin type approximation theorem, modulus of continuity, Lipschitz class functionals
Categories:41A25, 41A36

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