Bounds having Riemann type quantum integrals via strongly convex functions

Muhammad Aslam Noor; Gabriela Cristescu; Muhammad Uzair Awan

doi:10.1556/012.2017.54.2.1363

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 54: Issue 2

Bounds having Riemann type quantum integrals via strongly convex functions

Authors:

Muhammad Aslam Noor

Muhammad Aslam Noor Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan

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noormaslam@gmail.com

Gabriela Cristescu

Gabriela Cristescu Aurel Vlaicu University of Arad, Department of Mathematics and Computer Sciences, BD. Revolutiei, No. 77, 310130-Arad, Romania

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gabriela.cristescu@uav.ro

, and

Muhammad Uzair Awan

Muhammad Uzair Awan Department of Mathematics, Government College University, Faisalabad, Pakistan

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awan.uzair@gmail.com

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Pages:: 221–240

Online Publication Date:: Jun 2017

Publication Date:: 01 Jun 2017

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/012.2017.54.2.1363

Keywords:: Primary 26D15; 26A51; Convex; quantum calculus; inequalities; strongly convex function

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The aim of this paper is to obtain some new bounds having Riemann type quantum integrals within the class of strongly convex functions. The results obtained are sharp on limit q → 1. These new results reduce to Tariboon-Ntouyas, Merentes-Nikodem and other previously known results when q → 1, where 0 < q < 1. The sharpness of the results of Tariboon-Ntouyas and Merentes-Nikodem is proved as a consequence.

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Studia Scientiarum Mathematicarum Hungarica

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Studia Scientiarum Mathematicarum Hungarica
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