Some new integral inequalities of the Simpson type for MT-convex functions

In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity: Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.

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A new generalization of some quantum integral inequalities for quantum differentiable convex functions

Advances in Difference Equations ◽

10.1186/s13662-021-03382-0 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Yi-Xia Li ◽

Muhammad Aamir Ali ◽

Hüseyin Budak ◽

Mujahid Abbas ◽

Yu-Ming Chu

Keyword(s):

Integral Inequality ◽

Convex Functions ◽

Integral Identity ◽

Integral Inequalities ◽

Quantum Integral ◽

Special Cases

AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

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Some Hermite–Hadamard type integral inequalities for convex functions defined on convex bodies in ℝn\mathbb{R}^{n}

Journal of Applied Analysis ◽

10.1515/jaa-2020-2005 ◽

2020 ◽

Vol 26 (1) ◽

pp. 67-77 ◽

Cited By ~ 1

Author(s):

Silvestru Sever Dragomir

Keyword(s):

Euclidean Space ◽

Convex Functions ◽

Convex Bodies ◽

Integral Inequalities ◽

Divergence Theorem ◽

Several Variables ◽

Type Integral ◽

Bounded Convex

AbstractIn this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space {\mathbb{R}^{n}} for any {n\geq 2}.

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Some weighted integral inequalities for differentiable beta-convex functions

Journal of Interdisciplinary Mathematics ◽

10.1080/09720502.2021.1932858 ◽

2021 ◽

pp. 1-21

Author(s):

N. Azzouza ◽

B. Meftah

Keyword(s):

Convex Functions ◽

Integral Inequalities ◽

Weighted Integral

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New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

Mathematics ◽

10.3390/math9151753 ◽

2021 ◽

Vol 9 (15) ◽

pp. 1753

Author(s):

Saima Rashid ◽

Aasma Khalid ◽

Omar Bazighifan ◽

Georgia Irina Oros

Keyword(s):

Integral Operator ◽

Convex Functions ◽

Hypergeometric Functions ◽

Fractional Integral ◽

Type Inequality ◽

Fractional Integral Operator ◽

Integral Inequalities ◽

Convex Mappings ◽

Special Cases ◽

Harmonically Convex Functions

Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are ℘-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.

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New fractional inequalities of Hermite–Hadamard type involving the incomplete gamma functions

Journal of Inequalities and Applications ◽

10.1186/s13660-020-02538-y ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Pshtiwan Othman Mohammed ◽

Thabet Abdeljawad ◽

Dumitru Baleanu ◽

Artion Kashuri ◽

Faraidun Hamasalh ◽

...

Keyword(s):

Convex Functions ◽

Special Functions ◽

Integral Inequalities ◽

Fractional Operators ◽

Gamma Functions ◽

Incomplete Gamma Functions ◽

Type Integral

AbstractA specific type of convex functions is discussed. By examining this, we investigate new Hermite–Hadamard type integral inequalities for the Riemann–Liouville fractional operators involving the generalized incomplete gamma functions. Finally, we expose some examples of special functions to support the usefulness and effectiveness of our results.

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