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By extending the classical quantitative approximation results for positiveand linear operators in $L^{p}([0, 1]), 1\le p \le +\infty$ of Berens andDeVore in 1978 and of Swetits and Wood in 1983 to the more general case ofsublinear, monotone and strongly translatable operators, in this paper weobtain quantitative estimates in terms of the second order and third ordermoduli of smoothness, in Korovkin type theorems. Applications to concreteexamples are included and an open question concerning interpolation theory forsublinear, monotone and strongly translatable operators is raised.

Quantitative Korovkin theorems for sublinear, monotone and strongly translatable operators in $L^{p}([0, 1]), 1\le p \le +\infty$