Document Type : Research Paper

Authors

• Artion Kashuri ¹
• Muhammad Aamir Ali ²
• Mujahid Abbas ³
• Huseyin BUDAK ⁴

¹ Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, 9400, Vlora, Albania

² Department of Mathematics Government College University Faisalabad Sahiwal Campus, Pakistan

³ Department of Mathematics, Government College University, Lahore 54000, Pakistan and Department of Mathematics and Applied, Mathematics, University of Pretoria, Lynnwood road, Pretoria 0002, South Africa

⁴ Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce, Turkey

Abstract

In the present work, we prove a parametrized identity for a differentiable function via generalized integral operators. By applying the established identity and the new so-called generalized m-convex function, some generalized trapezium, Ostrowski and Simpson type integral inequalities have been discovered. Various special cases have been studied as well. Some applications of the present results to special means and new error estimates for the trapezium and midpoint quadrature formula have been investigated. It is hoped that the methods and techniques of this paper could further stimulate the research conducted in the field of integral inequalities.

Keywords

• Trapezium inequality
• Ostrowski inequality
• Simpson inequality
• convexity
• general fractional integrals