We analyze a general concept of limiters for a high order DG scheme written for a 1-D problem. The limiters, which are local and do not require extended stencils, are incorporated into the solution reconstruction in order to meet the requirement of monotonicity and avoid spurious solution overshoots. A limiter
will be defined based on the solution jumps at grid interfaces. It will be shown that
should be 0 <
< 1 for a monotone approximate solution.