q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions

By Necmettin Alp, M. Sarıkaya, M. Kunt, Imdat Iscan. 2016

238 citations recorded by the source corpus.

In this paper, we prove the correct q-Hermite–Hadamard inequality, some new q-Hermite–Hadamard inequalities, and generalized q-Hermite–Hadamard inequality. By using the left hand part of the correct q-Hermite–Hadamard inequality, we have a new equality. Finally using the new equality, we give some q-midpoint type integral inequalities through q-differentiable convex and q-differentiable quasi-convex functions. Many results given in this paper provide extensions of others given in previous works.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/df4149a3518398e4dac9683de362f85334b1bb16

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In Applied Mathematics

Citations in the corpus

$$\left( p,q\right) $$p,q-Hermite–Hadamard inequalities and $$\left( p,q\right) $$p,q-estimates for midpoint type inequalities via convex and quasi-convex functions (2018, methodology): “gave the q-Hermite–Hadamard inequality as follows: Theorem 1 [2] (q-Hermite–Hadamard inequality) Let f : [a, b] → R be a convex differentiable function on [a, b] and 0 < q < 1.”
On q-Hermite-Hadamard Inequalities for Differentiable Convex Functions (2019, background): “[32] studied the q-analogue of Hermite–Hadamard’s inequality for increasing functions, that is, f ( qa + b 1 + q ) ≤ 1 b− a ∫ b”