Jensen's type inequalities for the finite Hilbert transform of convex functions

In this paper we obtain some new inequalities for the finite Hilbert transform of convex functions by the use of Jensen’s integral inequality. Applications for exponential function are provided as well.

Download Full-text

Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means

Journal of Function Spaces and Applications ◽

10.1155/2012/980438 ◽

2012 ◽

Vol 2012 ◽

pp. 1-14 ◽

Cited By ~ 21

Author(s):

Bo-Yan Xi ◽

Feng Qi

Keyword(s):

Integral Inequality ◽

Convex Functions ◽

Integral Inequalities ◽

Special Means ◽

New Inequalities

The authors establish some new inequalities for differentiable convex functions, which are similar to the celebrated Hermite-Hadamard's integral inequality for convex functions, and apply these inequalities to construct inequalities for special means of two positive numbers.

Download Full-text

Some new inequalities for convex functions via generalized integral operators and their applications

Mathematica ◽

10.24193/mathcluj.2021.2.12 ◽

2021 ◽

Vol 63 (86) (2) ◽

pp. 268-283

Author(s):

Artion Kashuri ◽

◽

Themistocles M. Rassias ◽

Keyword(s):

Integral Equation ◽

Integral Operator ◽

Error Estimates ◽

Integral Inequality ◽

Convex Functions ◽

Integral Operators ◽

Absolute Value ◽

Special Means ◽

Type Integral ◽

New Inequalities

The authors discover an identity for a generalized integral operator via differentiable function. By using this integral equation, we derive some new bounds on Hermite–Hadamard type integral inequality for differentiable mappings that are in absolute value at certain powers convex. Our results include several new and known results as particular cases. At the end, some applications of presented results for special means and error estimates for the mixed trapezium and midpoint formula have been analyzed. The ideas and techniques of this paper may stimulate further research in the field of integral inequalities.

Download Full-text

Hermite–Hadamard Type Inequalities Involving k-Fractional Operator for (h¯,m)-Convex Functions

Symmetry ◽

10.3390/sym13091686 ◽

2021 ◽

Vol 13 (9) ◽

pp. 1686 ◽

Cited By ~ 2

Author(s):

Soubhagya Kumar Sahoo ◽

Hijaz Ahmad ◽

Muhammad Tariq ◽

Bibhakar Kodamasingh ◽

Hassen Aydi ◽

...

Keyword(s):

Integral Inequality ◽

Convex Functions ◽

Fractional Integral ◽

Special Functions ◽

Fractional Operator ◽

Hadamard’S Inequality ◽

Integral Equality ◽

Symmetric Property ◽

New Inequalities

The principal motivation of this paper is to establish a new integral equality related to k-Riemann Liouville fractional operator. Employing this equality, we present several new inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard integral inequality. Additionally, some novel cases of the established results for different kinds of convex functions are derived. This fractional integral sums up Riemann–Liouville and Hermite–Hadamard’s inequality, which have a symmetric property. Scientific inequalities of this nature and, particularly, the methods included have applications in different fields in which symmetry plays a notable role. Finally, applications of q-digamma and q-polygamma special functions are presented.

Download Full-text

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.

Download Full-text

Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

Journal of Inequalities and Applications ◽

10.1186/s13660-020-02488-5 ◽

2020 ◽

Vol 2020 (1) ◽

Cited By ~ 1

Author(s):

Dafang Zhao ◽

Muhammad Aamir Ali ◽

Artion Kashuri ◽

Hüseyin Budak ◽

Mehmet Zeki Sarikaya

Keyword(s):

Convex Functions ◽

Fractional Integrals ◽

Special Cases ◽

Definition Of ◽

The Given ◽

Class Of Functions ◽

Interval Valued ◽

New Inequalities

Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

Download Full-text

Post-quantum Hermite–Hadamard type inequalities for interval-valued convex functions

Journal of Inequalities and Applications ◽

10.1186/s13660-021-02619-6 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Muhammad Aamir Ali ◽

Hüseyin Budak ◽

Ghulam Murtaza ◽

Yu-Ming Chu

Keyword(s):

Convex Functions ◽

Fundamental Properties ◽

Interval Valued ◽

New Inequalities

AbstractIn this research, we introduce the notions of $(p,q)$ ( p , q ) -derivative and integral for interval-valued functions and discuss their fundamental properties. After that, we prove some new inequalities of Hermite–Hadamard type for interval-valued convex functions employing the newly defined integral and derivative. Moreover, we find the estimates for the newly proved inequalities of Hermite–Hadamard type. It is also shown that the results proved in this study are the generalization of some already proved research in the field of Hermite–Hadamard inequalities.

Download Full-text