Moving Averages that Preserve the Monotonicity of Quotients

There are operators that have the property that when applied to both the numerator and the denominator of a monotonic quotient of functions or sequences produce another monotonic quotient. Such operations have been very useful to study several problems, including various types of inequalities. Here we study when moving averages preserve the monotonicity of quotients of sequences and quotients of functions. We give results on the averages that guarantee the preservation of monotonicity and examples where monotonicity is not preserved.