• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.213-223
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• 2004

Double integral inequalities of Simpson type are obtained. These inequalities are sharp. Applications in numerical integration are given.

• Korean Journal of Mathematics
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• 제29권1호
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• pp.193-209
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• 2021

In this research, we offer two new quantum integral equalities for recently defined qε2-integral and derivative, the derived equalities then used to prove quantum integral inequalities of Simpson's and Newton's type for preinvex functions. We also considered the special cases of established results and offer several new and existing results inside the literature of Simpson's and Newton's type inequalities.

• Korean Journal of Mathematics
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• 제31권2호
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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.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.279-295
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• 2019

In this paper, using local fractional integrals on fractal sets $R^{\alpha}(0<{\alpha}{\leq}1)$ of real line numbers, we establish new some inequalities of Simpson's type based on generalized convexity.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.47-56
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• 2024

It is well known that inequalities enable us to analyze and solve complex problems with precision and efficiency. The inequalities provide powerful tools for establishing bounds, optimizing solutions, and deepening our understanding of mathematical concepts, paving the way for advancements in areas such as optimization, analysis, and probability theory. In this paper, we present some properties for Hadamard-Simpsons type inequalities in the classic integral and Riemann-Liouville fractional integral. We use the convexity of the given function and its first derivative.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.65-79
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• 2007

An optimal 3-point quadrature formula of closed type is derived. It is shown that the optimal quadrature formula has a better error bound than the well-known Simpson's rule. A corrected formula is also considered. Various error inequalities for these formulas are established. Applications in numerical integration are given.

• 호남수학학술지
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• 제45권1호
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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.