Abstract
In this paper, variant inequalities of Ostrowski’s type for absolutely continuous mappings whose derivatives are monotonic, belongs to L1[a, b], Lq[a, b], (q > 1) and L∞[a, b] are established.
Highlights
In 1938, Ostrowski established a very interesting inequality for differentiable mappings with bounded derivatives, as follows [6]: Theorem 1.1
1 4 is the best possible in the sense that it cannot be replaced by a smaller constant
The reader may be refer to the monograph [6] where various inequalities of Ostrowski type are discussed
Summary
In 1938, Ostrowski established a very interesting inequality for differentiable mappings with bounded derivatives, as follows [6]: Theorem 1.1. In [5], Guessab and Schmeisser have proved among others, the following companion of Ostrowski’s inequality: Theorem 1.2. The inequality is best in the sense that it cannot be replaced by a smaller constant. Companions of Ostrowski’s integral inequality for absolutely continuous functions was considered by Dragomir in [7], as follows : Theorem 1.3. Liu [9], introduced some companions of an Ostrowski type integral inequality for functions whose derivatives are absolutely continuous. The aim of this paper is to study the companion of Ostrowski inequality (1.2) for the class of functions whose derivatives in absolutely continuous
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