scholarly journals On New Generalized Dunkel Type Integral Inequalities with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1576
Author(s):  
Dong-Sheng Wang ◽  
Huan-Nan Shi ◽  
Chun-Ru Fu ◽  
Wei-Shih Du
Keyword(s):  
Integral Inequality ◽  
Integral Inequalities ◽  
Inequality Theory ◽  
Type Integral ◽  
Schur Convexity

In this paper, by applying majorization theory, we study the Schur convexity of functions related to Dunkel integral inequality. We establish some new generalized Dunkel type integral inequalities and their applications to inequality theory.

scholarly journals On a relation to two basic Hilbert-type integral inequalities

2009 ◽  
Vol 40 (3) ◽  
pp. 217-223 ◽  
Author(s):  
Bicheng Yang
Keyword(s):  
Weight Function ◽  
Integral Inequality ◽  
Equivalent Form ◽  
Constant Factor ◽  
Integral Inequalities ◽  
Real Analysis ◽  
Best Constant ◽  
Type Integral ◽  
Best Constant Factor ◽  
Hilbert Type

In this paper, by using the way of weight function and the technic of real analysis, a new integral inequality with some parameters and a best constant factor is given, which is a relation to two basic Hilbert-type integral inequalities. The equivalent form and the reverse forms are considered.

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 Some Opial-type integral inequalities via $(p,q)$-calculus

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Md. Nasiruzzaman ◽  
Aiman Mukheimer ◽  
M. Mursaleen
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Type Integral

AbstractIn this paper, we introduce a new Opial-type inequality by using $(p,q)$(p,q)-calculus and establish some integral inequalities. We find a $(p,q)$(p,q)-generalization of a Steffensens-type integral inequality and some other inequalities.

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.

Some weighted integral inequalities for differentiable h-preinvex functions

2018 ◽  
Vol 25 (3) ◽  
pp. 441-450 ◽  
Author(s):  
Muhammad Amer Latif ◽  
Sever Silvestru Dragomir ◽  
Ebrahim Momoniat
Keyword(s):  
Integral Inequality ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Absolute Value ◽  
Type Integral ◽  
Weighted Integral ◽  
Preinvex Functions ◽  
Special Case

AbstractIn this paper, by using a weighted identity for functions defined on an open invex subset of the set of real numbers, by using the Hölder integral inequality and by using the notion of h-preinvexity, we present weighted integral inequalities of Hermite–Hadamard-type for functions whose derivatives in absolute value raised to certain powers are h-preinvex functions. Some new Hermite–Hadamard-type integral inequalities are obtained when h is super-additive. Inequalities of Hermite–Hadamard-type for s-preinvex functions are given as well as a special case of our results.

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 q-Hardy type inequalities for quantum integrals

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Necmettin Alp ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Hardy Inequality ◽  
Integral Inequality ◽  
Integral Inequalities ◽  
Hardy Type Inequalities ◽  
Quantum Calculus ◽  
Quantum Numbers ◽  
Hardy Type ◽  
Type Integral ◽  
The Hardy Inequality

AbstractThe aim of this work is to obtain quantum estimates for q-Hardy type integral inequalities on quantum calculus. For this, we establish new identities including quantum derivatives and quantum numbers. After that, we prove a generalized q-Minkowski integral inequality. Finally, with the help of the obtained equalities and the generalized q-Minkowski integral inequality, we obtain the results we want. The outcomes presented in this paper are q-extensions and q-generalizations of the comparable results in the literature on inequalities. Additionally, by taking the limit $q\rightarrow 1^{-}$ q → 1 − , our results give classical results on the Hardy inequality.

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>

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