$$\left( p,q\right) $$p,q-Hermite–Hadamard inequalities and $$\left( p,q\right) $$p,q-estimates for midpoint type inequalities via convex and quasi-convex functions

By M. Kunt, Imdat Iscan, Necmettin Alp, M. Sarıkaya. 2018

57 citations recorded by the source corpus.

In this paper, we prove the correct $$\left( p,q\right) $$p,q-Hermite–Hadamard inequality, some new $$\left( p,q\right) $$p,q-Hermite–Hadamard inequalities, and generalized $$\left( p,q\right) $$p,q-Hermite–Hadamard inequality. By using the left hand part of the correct $$\left( p,q\right) $$p,q-Hermite–Hadamard inequality, we have a new equality. Finally using the new equality, we give some $$\left( p,q\right) $$p,q-midpoint type integral inequalities through $$\left( p,q\right) $$p,q-differentiable convex and $$\left( p,q\right) $$p,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/21360ecb17c8401b2aad26d6e709a14b0c407357