Abstract
Abstract In this paper, we first prove an identity for twice quantum differentiable functions. Then, by utilizing the convexity of ∣ D q 2 b f ∣ | {}^{b}D_{q}^{2}\hspace{0.08em}f| and ∣ D q 2 a f ∣ | {}_{a}D_{q}^{2}\hspace{0.08em}f| , we establish some quantum Ostrowski inequalities for twice quantum differentiable mappings involving q a {q}_{a} and q b {q}^{b} -quantum integrals. The results presented here are the generalization of already published ones.
Highlights
The study of various types of integral inequalities has been the focus of great attention for well over a century by a number of mathematicians, interested in both pure and applied mathematics
One of the many fundamental mathematical discoveries of Ostrowski [1] is the following classical integral inequality associated with the differentiable mappings: Theorem 1.1
If the assumptions of Lemma 3.1 hold, we have the following inequality provided that ∣bDq2 f ∣ and ∣a Dq2 f ∣ are convex on [a, b]
Summary
The study of various types of integral inequalities has been the focus of great attention for well over a century by a number of mathematicians, interested in both pure and applied mathematics. Many studies have recently been carried out in the field of q-analysis, starting with Euler due to a high demand for mathematics that models quantum computing q-calculus appeared as a connection between mathematics and physics. It has several applications in different mathematical areas such as number theory, combinatorics, orthogonal polynomials, basic hypergeometric functions, and other sciences, quantum theory, mechanics, and the theory of relativity [13,14,15,16]. For more results in this direction, the readers may refer to [8,13,14,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38]
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