Electron. J. Differential Equations,
Vol. 2018 (2018), No. 112, pp. 1-11.
On q-Steffensen inequality
Predrag Rajkovic, Miomir Stankovic, Sladjana Marinkovic, Mokhtar Kirane
Abstract:
In this article, we study an analogue of the classical integral inequality
established by Steffensen in q-calculus. The difficulties ensued form
differences between the classical and q-integral. We exceed them in
two directions: firstly, by restricting the area of parameter q, and
another by modifying the expression of the original inequality.
We establish the conditions which guarantee their holding on. Finally,
we illustrate our considerations by the examples.
Submitted March 1, 2018. Published May 10, 2018.
Math Subject Classifications: 33D60, 26D15.
Key Words: q-integral; nonnegativity; integral inequality.
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Predrag M. Rajkovic
Department of Mathematics and Informatics
Faculty of Mechanical Engineering, University of Nis
Nis 18000, Serbia
email: pedja.rajk@gmail.com
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Miomir S. Stankovic
Department of Mathematics
Faculty of Occupation Safety,
University of Nis
Nis 18000, Serbia
email: miomir.stankovic@gmail.com
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Sladjana D. Marinkovic
Department of Mathematics
Faculty of Electronic Engineering, University of Nis
Nis 18000, Serbia
email: sladjana.marinkovic@elfak.ni.ac.rs
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Mokhtar Kirane
LaSIE, Faculte des Sciences et Technologies
Universite de La Rochelle
Avenue M. Crepeau, 17042 La Rochelle, France
email: mokhtar.kirane@univ-lr.fr
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