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A new extension of quantum Simpson's and quantum Newton's type inequalities for quantum differentiable convex functions
  • Muhammad Aamir Ali,
  • Hüseyin BUDAK,
  • Zhiyue Zhang
Muhammad Aamir Ali
Nanjing Normal University School of Mathematical Sciences

Corresponding Author:mahr.muhammad.aamir@gmail.com

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Hüseyin BUDAK
Düzce University
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Zhiyue Zhang
Nanjing Normal University School of Mathematical Sciences
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Abstract

In this paper, we prove two identities involving quantum derivatives, quantum integrals, and certain parameters. Using the newly proved identities, we prove new inequalities of Simpson's and Newton's type for quantum differentiable convex functions under certain assumptions. Moreover, we discuss the special cases of our main results and obtain some new and existing Simpson's type inequalities, Newton's type inequalities, midpoint type inequalities and trapezoidal type inequalities.
15 Feb 2021Submitted to Mathematical Methods in the Applied Sciences
16 Feb 2021Submission Checks Completed
16 Feb 2021Assigned to Editor
22 Feb 2021Reviewer(s) Assigned
16 Aug 2021Review(s) Completed, Editorial Evaluation Pending
08 Sep 2021Editorial Decision: Revise Major
14 Sep 20211st Revision Received
14 Sep 2021Submission Checks Completed
14 Sep 2021Assigned to Editor
17 Sep 2021Reviewer(s) Assigned
20 Sep 2021Review(s) Completed, Editorial Evaluation Pending
20 Sep 2021Editorial Decision: Accept
15 Mar 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 4 on pages 1845-1863. 10.1002/mma.7889