Open Mathematics (Jun 2021)

Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus

  • Ali Muhammad Aamir,
  • Budak Hüseyin,
  • Akkurt Abdullah,
  • Chu Yu-Ming

DOI
https://doi.org/10.1515/math-2021-0020
Journal volume & issue
Vol. 19, no. 1
pp. 440 – 449

Abstract

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In this paper, we first prove an identity for twice quantum differentiable functions. Then, by utilizing the convexity of ∣Dq2bf∣| {}^{b}D_{q}^{2}\hspace{0.08em}f| and ∣Dq2af∣| {}_{a}D_{q}^{2}\hspace{0.08em}f| , we establish some quantum Ostrowski inequalities for twice quantum differentiable mappings involving qa{q}_{a} and qb{q}^{b}-quantum integrals. The results presented here are the generalization of already published ones.

Keywords