Open Mathematics (Jun 2021)
Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus
Abstract
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.
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