Abstract
In this paper, we prove a new quantum integral equality involving a parameter, left and right quantum derivatives. Then, we use the newly established equality and prove some new estimates of quantum Ostrowski, quantum midpoint, quantum trapezoidal and quantum Simpson’s type inequalities for q-differentiable convex functions. It is also shown that the newly established inequalities are the refinements of the existing inequalities inside the literature. Finally, some examples and applications are given to illustrate the investigated results.
Highlights
1938, which became known as the Ostrowski inequality [1]
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Inspired by the ongoing studies, we prove a new parameterized quantum integral identity involving left and right quantum derivatives to prove different variants of quantum integral inequalities for quantum differentiable convex functions
Summary
In [7], Alp et al proved the following version of quantum Hermite–Hadamard type for convex functions using the left quantum integrals: Theorem 3. Bermudo et al [8] used the right quantum integrals and proved the following variant of Hermite–Hadamard type inequalities for convex functions: Theorem 4. Some authors generalized the quantum Hermite–Hadamard inequalities for coordinated convex functions in [18,19,20]. Inspired by the ongoing studies, we prove a new parameterized quantum integral identity involving left and right quantum derivatives to prove different variants of quantum integral inequalities for quantum differentiable convex functions.
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