• Honam Mathematical Journal
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• v.45 no.1
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• pp.160-183
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• 2023

In the present paper, we prove that our main inequality reduces to some trapezoid and Newton type inequalities for differentiable s-convex functions. These inequalities are established by using the well-known Riemann-Liouville fractional integrals. With the help of special cases of our main results, we also present some new and previously obtained trapezoid and Newton type inequalities.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.239-250
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• 2018

In this paper, we establish some new Newton's type integral inequalities for p-harmonic convex functions. Some special cases are also discussed as applications of our main results. Results obtained in this paper may be starting point for further research.

• Korean Journal of Mathematics
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• v.31 no.2
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• pp.161-180
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• 2023

In this article, we will utilize (α, m)-convexity to create a new form of Simpson-Newton inequalities in quantum calculus by using q_𝝔1-integral and q_𝝔1-derivative. Newly discovered inequalities can be transformed into quantum Newton and quantum Simpson for generalized convexity. Additionally, this article demonstrates how some recently created inequalities are simply the extensions of some previously existing inequalities. The main findings are generalizations of numerous results that already exist in the literature, and some fundamental inequalities, such as Hölder's and Power mean, have been used to acquire new bounds.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.325-338
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• 2022

In this paper, a new identity is given. On the basis of this identity, we establish some new estimates of Milne's quadrature rule, for functions whose first derivative is s-convex. We discuss the cases where the derivatives are bounded as well as Lipschitzian. Some illustrative applications are given.