NEW GENERALIZED OSTROWSKI-TYPE INEQUALITIES INVOLVING INTEGRAL MEANS OVER END INTERVALS

Abstract

In this paper, we establish a new Ostrowski-type inequality involving integral means over end intervals by introducing a generalized Montgomery-type identity and a generalized Peano kernel. The obtained inequality provides an explicit estimate for twice differentiable functions under the boundedness assumption on the second derivative. Furthermore, some important special cases are discussed to illustrate the applicability of the proposed result. The developed inequality extends and generalizes existing Ostrowski-type inequalities and may be useful in numerical integration, approximation theory, and error estimation.

Keywords

Ostrowski inequality; Integral means; Montgomery identity; Peano kernel; Numerical integration; Approximation theory.