scholarly journals Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Saad Ihsan Butt ◽  
Praveen Agarwal ◽  
Saba Yousaf ◽  
Juan L. G. Guirao
Keyword(s):  
Probability Density Function ◽  
Convex Function ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integrals ◽  
Fractal Sets ◽  
Local Fractional Integral ◽  
Fractal Space ◽  
Harmonic Convex ◽  
Harmonically Convex Function

AbstractIn this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized Jensen–Mercer inequality involving local fractional integrals is obtained. Moreover, we establish some generalized Jensen–Mercer-type local fractional integral inequalities for harmonically convex function. Also, we obtain some generalized related results using these inequalities on the fractal space. Finally, we give applications of generalized means and probability density function.

scholarly journals New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 568
Author(s):  
Ohud Almutairi ◽  
Adem Kılıçman
Keyword(s):  
Convex Function ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Absolute Value ◽  
Fractal Sets ◽  
Related Integral ◽  
Generalized Fractional Integral ◽  
Symmetric Property ◽  
Point Type

In this paper, a new identity for the generalized fractional integral is defined. Using this identity we studied a new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. This fractional integral generalizes Riemann-Liouville and Hadamard’s integral, which possess a symmetric property. We derive trapezoid and mid-point type inequalities connected to this generalized Hermite-Hadamard inequality.

scholarly journals New Generalized the Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals

2020 ◽  
Author(s):  
Ohud Almutairi ◽  
Adem Kılıçman
Keyword(s):  
Convex Function ◽  
Integral Inequality ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Absolute Value ◽  
Fractal Sets ◽  
Related Integral ◽  
Generalized Fractional Integral ◽  
Point Type

In this paper, a new identity for the generalized fractional integral is defined, through which new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. We derive trapezoid and mid-point type inequalities connected to these generalized Hermite-Hadamard inequality.

scholarly journals Some Midpoint Inequalities for η -Convex Function via Weighted Fractional Integrals

2022 ◽  
Vol 2022 ◽  
pp. 1-12
Author(s):  
Lei Chen ◽  
Waqas Nazeer ◽  
Farman Ali ◽  
Thongchai Botmart ◽  
Sarah Mehfooz
Keyword(s):  
Convex Function ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integrals ◽  
Special Cases

In this research, by using a weighted fractional integral, we establish a midpoint version of Hermite-Hadamrad Fejér type inequality for η -convex function on a specific interval. To confirm the validity, we considered some special cases of our results and relate them with already existing results. It can be observed that several existing results are special cases of our presented results.

scholarly journals Some new Hermite-Hadamard type inequalities for generalized harmonically convex functions involving local fractional integrals

2021 ◽  
Vol 6 (10) ◽  
pp. 10679-10695
Author(s):  
Wenbing Sun ◽  
◽  
Rui Xu
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Fractal Sets ◽  
Special Means ◽  
Local Fractional Integral ◽  
Harmonically Convex Functions

<abstract><p>In this paper, we establish a new integral identity involving local fractional integral on Yang's fractal sets. Using this integral identity, some new generalized Hermite-Hadamard type inequalities whose function is monotonically increasing and generalized harmonically convex are obtained. Finally, we construct some generalized special means to explain the applications of these inequalities.</p></abstract>

scholarly journals Fractional Hermite–Hadamard–Fejer Inequalities for a Convex Function with Respect to an Increasing Function Involving a Positive Weighted Symmetric Function

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1503 ◽  
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Artion Kashuri
Keyword(s):  
Fractional Calculus ◽  
Convex Function ◽  
Symmetric Function ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Fractional Operators ◽  
Important Direction ◽  
Increasing Function

There have been many different definitions of fractional calculus presented in the literature, especially in recent years. These definitions can be classified into groups with similar properties. An important direction of research has involved proving inequalities for fractional integrals of particular types of functions, such as Hermite–Hadamard–Fejer (HHF) inequalities and related results. Here we consider some HHF fractional integral inequalities and related results for a class of fractional operators (namely, the weighted fractional operators), which apply to function of convex type with respect to an increasing function involving a positive weighted symmetric function. We can conclude that all derived inequalities in our study generalize numerous well-known inequalities involving both classical and Riemann–Liouville fractional integral inequalities.

scholarly journals Hermite-Hadamard type inequalities for generalized convex functions on fractal sets style

2018 ◽  
Vol 38 (1) ◽  
pp. 101-116 ◽  
Author(s):  
Muharrem Tomar ◽  
Praveen Agarwal ◽  
Junesang Choi
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Generalized Convex Functions ◽  
Fractal Sets ◽  
Special Cases ◽  
Logarithmic Means ◽  
Local Fractional Integral ◽  
Generalized Arithmetic

We aim to  establish certain generalized Hermite-Hadamard's inequalities for generalized convex functions via local fractional integral. As special cases of some of the results presented here, certain interesting inequalities involving generalized arithmetic and logarithmic means are obtained.

scholarly journals Fractional version of the Jensen-Mercer and Hermite-Jensen-Mercer type inequalities for strongly h-convex function

2021 ◽  
Vol 7 (1) ◽  
pp. 784-803
Author(s):  
Fangfang Ma ◽  
Keyword(s):  
Convex Function ◽  
Integral Inequality ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Definition Of

<abstract><p>In this paper we find further versions of generalized Hadamard type fractional integral inequality for $ k $-fractional integrals. For this purpose we utilize the definition of $ h $-convex function. The presented results hold simultaneously for variant types of convexities and fractional integrals.</p></abstract>

scholarly journals On Hadamard Type Fractional Inequalities for Riemann–Liouville Integrals via a Generalized Convexity

2022 ◽  
Vol 6 (1) ◽  
pp. 28
Author(s):  
Tao Yan ◽  
Ghulam Farid ◽  
Hafsa Yasmeen ◽  
Chahn Yong Jung
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Generalized Convexity ◽  
Monotone Function ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Hadamard Inequality

In the literature of mathematical inequalities, convex functions of different kinds are used for the extension of classical Hadamard inequality. Fractional integral versions of the Hadamard inequality are also studied extensively by applying Riemann–Liouville fractional integrals. In this article, we define (α,h−m)-convex function with respect to a strictly monotone function that unifies several types of convexities defined in recent past. We establish fractional integral inequalities for this generalized convexity via Riemann–Liouville fractional integrals. The outcomes of this work contain compact formulas for fractional integral inequalities which generate results for different kinds of convex functions.

scholarly journals Some Estimates for Generalized Riemann-Liouville Fractional Integrals of Exponentially Convex Functions and Their Applications

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 807 ◽  
Author(s):  
Saima Rashid ◽  
Thabet Abdeljawad ◽  
Fahd Jarad ◽  
Muhammad Aslam Noor
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Order Derivative ◽  
Fundamental Identity ◽  
First Order ◽  
Special Means ◽  
Exponentially Convex Functions ◽  
New Inequalities

In the present paper, we investigate some Hermite-Hadamard ( HH ) inequalities related to generalized Riemann-Liouville fractional integral ( GRLFI ) via exponentially convex functions. We also show the fundamental identity for GRLFI having the first order derivative of a given exponentially convex function. Monotonicity and exponentially convexity of functions are used with some traditional and forthright inequalities. In the application part, we give examples and new inequalities for the special means.

Applications of Yang-Fourier Transform to Local Fractional Equations with Local Fractional Derivative and Local Fractional Integral

2012 ◽  
Vol 461 ◽  
pp. 306-310 ◽  
Author(s):  
Wei Ping Zhong ◽  
Feng Gao ◽  
Xiao Ming Shen
Keyword(s):  
Fourier Transform ◽  
Fractional Derivative ◽  
Fractional Integral ◽  
Fractional Fourier Transform ◽  
Local Fractional Derivative ◽  
Fractional Equations ◽  
Local Fractional Integral ◽  
Fractal Space

Yang-Fourier transform is the generalization of the fractional Fourier transform of non-differential functions on fractal space. In this paper, we show applications of Yang-Fourier transform to local fractional equations with local fractional derivative and local fractional integral

Sign in / Sign up

Export Citation Format

Share Document