scholarly journals Generalizations of Hermite–Hadamard Type Integral Inequalities for Convex Functions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 136
Author(s):  
Ying Wu ◽  
Hong-Ping Yin ◽  
Bai-Ni Guo
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Type Integral ◽  
Integral Identities

In the paper, with the help of two known integral identities and by virtue of the classical Hölder integral inequality, the authors establish several new integral inequalities of the Hermite–Hadamard type for convex functions. These newly established inequalities generalize some known results.

scholarly journals Fejér type integral inequalities related with geometrically-arithmetically convex functions with applications

2019 ◽  
Vol 23 (1) ◽  
pp. 51-64
Author(s):  
S. S. Dragomir ◽  
M. A. Latif ◽  
E. Momoniat
Keyword(s):  
Differentiable Function ◽  
Integral Inequality ◽  
Convex Functions ◽  
Symmetric Function ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Left Part ◽  
Special Means ◽  
Type Integral

A new identity involving a geometrically symmetric function and a differentiable function is established. Some new Fejér type integral inequalities, connected with the left part of Hermite–Hadamard type inequalities for geometrically-arithmetically convex functions, are presented by using the Hölder integral inequality and the notion of geometrically-arithmetically convexity. Applications of our results to special means of positive real numbers are given.

scholarly journals Some Fejér type integral inequalities for geometrically-arithmetically-convex functions with applications

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2193-2206 ◽  
Author(s):  
Muhammad Latif ◽  
Sever Dragomir ◽  
Ebrahim Momoniat
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Symmetric Functions ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Type Integral

In this paper, the notion of geometrically symmetric functions is introduced. A new identity involving geometrically symmetric functions is established, and by using the obtained identity, the H?lder integral inequality and the notion of geometrically-arithmetically convexity, some new Fej?r type integral inequalities are presented. Applications of our results to special means of positive real numbers are given as well.

scholarly journals Novel Analysis of Hermite–Hadamard Type Integral Inequalities via Generalized Exponential Type m-Convex Functions

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 31
Author(s):  
Muhammad Tariq ◽  
Hijaz Ahmad ◽  
Clemente Cesarano ◽  
Hanaa Abu-Zinadah ◽  
Ahmed E. Abouelregal ◽  
...  
Keyword(s):  
Exponential Type ◽  
Convex Functions ◽  
Integral Inequalities ◽  
The Novel ◽  
New Family ◽  
Algebraic Properties ◽  
Type Integral ◽  
Mathematical Sciences ◽  
Integral Identities ◽  
Intense Research

The theory of convexity has a rich and paramount history and has been the interest of intense research for longer than a century in mathematics. It has not just fascinating and profound outcomes in different branches of engineering and mathematical sciences, it also has plenty of uses because of its geometrical interpretation and definition. It also provides numerical quadrature rules and tools for researchers to tackle and solve a wide class of related and unrelated problems. The main focus of this paper is to introduce and explore the concept of a new family of convex functions namely generalized exponential type m-convex functions. Further, to upgrade its numerical significance, we present some of its algebraic properties. Using the newly introduced definition, we investigate the novel version of Hermite–Hadamard type integral inequality. Furthermore, we establish some integral identities, and employing these identities, we present several new Hermite–Hadamard H–H type integral inequalities for generalized exponential type m-convex functions. These new results yield some generalizations of the prior results in the literature.

scholarly journals Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus

2021 ◽  
Vol 7 (3) ◽  
pp. 4266-4292
Author(s):  
Jorge E. Macías-Díaz ◽  
◽  
Muhammad Bilal Khan ◽  
Muhammad Aslam Noor ◽  
Abd Allah A. Mousa ◽  
...  
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
The Other ◽  
Integral Inequalities ◽  
Generalized Convex Functions ◽  
Type Integral ◽  
The Subject ◽  
Harmonically Convex Functions ◽  
Interval Valued

<abstract> <p>The importance of convex and non-convex functions in the study of optimization is widely established. The concept of convexity also plays a key part in the subject of inequalities due to the behavior of its definition. The principles of convexity and symmetry are inextricably linked. Because of the considerable association that has emerged between the two in recent years, we may apply what we learn from one to the other. In this study, first, Hermite-Hadamard type inequalities for LR-$ p $-convex interval-valued functions (LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic>) are constructed in this study. Second, for the product of p-convex various Hermite-Hadamard (<italic>HH</italic>) type integral inequalities are established. Similarly, we also obtain Hermite-Hadamard-Fejér (<italic>HH</italic>-Fejér) type integral inequality for LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic>. Finally, for LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic>, various discrete Schur's and Jensen's type inequalities are presented. Moreover, the results presented in this study are verified by useful nontrivial examples. Some of the results reported here for be LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic> are generalizations of prior results for convex and harmonically convex functions, as well as $ p $-convex functions.</p> </abstract>

scholarly journals A note on Hadamard type integral inequalities involving several log-convex functions

2005 ◽  
Vol 36 (1) ◽  
pp. 43-47 ◽  
Author(s):  
B. G. Pachpatte
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Type Integral

In this note, two new inegral inequalities of Hadamard type involving several differentiable log-convex functions are given. Two refinements of Hadamard's integral inequality for log-convex functions recently established by Dragomir are shown to be recaptured as special instances.

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

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.

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

2020 ◽  
Vol 26 (1) ◽  
pp. 67-77 ◽  
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}.

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

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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