Difference between revisions of "Mozyraska-Torres logarithm is negative on (0,1)"
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==Theorem== | ==Theorem== | ||
| − | Let $\mathbb{T}$ be a [[time scale]]. If $t \in (0,1) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) < 0$. | + | Let $\mathbb{T}$ be a [[time scale]]. If $t \in (0,1) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) < 0$, where $L_{\mathbb{T}}$ denotes the [[Mozyrska-Torres logarithm]]. |
==Proof== | ==Proof== | ||
==References== | ==References== | ||
| − | {{PaperReference|The Natural Logarithm on Time Scales| | + | {{PaperReference|The Natural Logarithm on Time Scales|2008|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=Mozyrska-Torres logarithm is increasing|next=Mozyrska-Torres logarithm is positive on (1,infinity)}} |
Revision as of 15:27, 21 October 2017
Theorem
Let $\mathbb{T}$ be a time scale. If $t \in (0,1) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) < 0$, where $L_{\mathbb{T}}$ denotes the Mozyrska-Torres logarithm.
Proof
References
Dorota Mozyrska and Delfim F. M. Torres: The Natural Logarithm on Time Scales (2008)... (previous)... (next)
