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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
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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.

Peer review status:UNDER REVIEW

15 Feb 2021Submitted to Mathematical Methods in the Applied Sciences
16 Feb 2021Assigned to Editor
16 Feb 2021Submission Checks Completed
22 Feb 2021Reviewer(s) Assigned