Abstract
Abstract In this paper, we prove a quantum version of Montgomery identity and prove some new Ostrowski-type inequalities for convex functions in the setting of quantum calculus. Moreover, we discuss several special cases of newly established inequalities and obtain different new and existing inequalities in the field of integral inequalities.
Highlights
Over the past few decades, different kinds of integral inequalities have drawn the attention of many mathematicians
The classical integral inequality associated with the differentiable mappings is as follows: Theorem 1
The purpose of this paper is to study Ostrowski-type inequalities for convex functions by applying newly defined concept of qν-integral
Summary
Over the past few decades, different kinds of integral inequalities have drawn the attention of many mathematicians. The classical integral inequality associated with the differentiable mappings is as follows: Theorem 1. [7] If the mapping F : [μ, ν] → is differentiable on (μ, ν) and integrable on [μ, ν], the following inequality holds: ν. [10, Lemma 1] Suppose that F : [μ, ν] → is differentiable on (μ, ν) and integrable on [μ, ν], the following equality holds: ν−κ ν. The purpose of this paper is to study Ostrowski-type inequalities for convex functions by applying newly defined concept of qν-integral. 1100 Thanin Sitthiwirattham et al. Ostrowski-type inequalities are obtained by using the Montgomery identity for qν-integral. We assume that the analysis initiated in this paper could provide researchers working on integral inequalities and their applications with a strong source of inspiration
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