Abstract

The purpose of this paper is to prove certain refinements of Ostrowski’s inequality in an inner product space. We study extensions of Ostrowski type inequalities in a 2-inner product space. Finally, some applications which are related to the Chebyshev function and the Grüss inequality are presented.

Highlights

  • In various fields of Mathematics the important applications are given using the inequalities in inner product spaces

  • In [8], Dragomir showed some improvements of the celebrated Cauchy–Schwarz inequality in complex inner product spaces

  • We show certain types of Ostrowski’s inequality in a 2-inner product space

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Summary

Introduction

In various fields of Mathematics the important applications are given using the inequalities in inner product spaces. A classic inequality in a complex inner product space X is the inequality of Cauchy–Schwarz [1], given by:. The inequality of Ostrowski in an inner product space over the field of complex numbers can be written as: kyk. In [8], Dragomir showed some improvements of the celebrated Cauchy–Schwarz inequality in complex inner product spaces. Let X = ( X, h·, ·i) be an inner product space over the field of real numbers (X is called Euclidean space) and let {e1 , e2 , ..., en } be an orthonormal system of vectors in X. The purpose of this paper is to prove certain refinements of Ostrowski’s inequality in an inner product space. We mention several conclusions about the development of other inequalities similar to Ostrowski’s inequality

Some Refinements of Ostrowski’s Inequality
Extensions of Several Inequalities to 2-Inner Product Spaces
Applications
Conclusions
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