Turing Machine to Accept String from a 3 character alphabet
One idea is to delete characters, to make it easier let me introduce @ character - it will denote empty space after scratching characters.
For example let input string be $BaabccB$, where $B$ is blank symbol.
At first check for $a$ and create state, say $qa$ which looks for $a$ and then replaces it with $@$ switches to $qb$ moves right until it finds $b$.
Then it replaces $b$ with $@$ switches state to $qc$ and moves right until it finds $c$.
Here again replaces $c$ with $@$ and switches to state $ql$ moves to the left until $a$ is found.
While moving right if blank symbol is encountered, it means that there are less symbols of particular character, this is good according to given language, if the next character is also missing otherwise it breaks inequality and we reject. Also when we seek $b$ but encounter $c$ we reject. After consecutive $c$ if there are other symbols, we reject (it is something like $abca$
When moving left, when blank is encountered, we are finished and accept.

It may happen that there are not sufficient number of $a$ or any character, so after reaching blank character we move right to delete $@$ characters. If we clear all and hit blank, we accept, otherwise we reject as some characters broke inequality.

Example: $BaabccB$
$B@abccB$ move right, switch state, replace $b$
$B@a@ccB$ move right, switch state, switch $c$.
$B@a@@cB$ move left until $a$ replace
$B@@@@cB$ move right, switch state, $c$ is encountered in $qb$ state, it means that $#c &gt; #b$ reject.

Excersise 1:
Try to solve similar question where $i \ge j \le k$

Excersise 2:
Try to solve similar question where $i = 2j = 3k$