A New Ostrowski Type Inequality Involving Integral Means Over End Intervals

The Ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The current article obtains bounds for the deviation of a function from a combination of integral means over the end intervals covering the entire interval. Perturbed expressions are also determined via the Chebychev functional. A variety of earlier results are recaptured as particular instances of the current development.