scholarly journals Hermite-Hadamard-Fejer type inequalities for s-convex function in the second sense via fractional integrals

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3131-3138 ◽  
Author(s):  
Erhan Set ◽  
İmdat İşcan ◽  
Hasan Kara
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integrals

In this paper, we established Hermite-Hadamard-Fejer type inequalities for s-convex functions in the second sense via fractional integrals. The some results presented here would provide extansions of those given in earlier works.

scholarly journals Conformable Fractional Integrals Versions of Hermite-Hadamard Inequalities and Their Generalizations

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Adil Khan ◽  
Yu-Ming Chu ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Gohar Ali
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integrals ◽  
Montgomery Identity

We prove new Hermite-Hadamard inequalities for conformable fractional integrals by using convex function, s-convex, and coordinate convex functions. We prove new Montgomery identity and by using this identity we obtain generalized Hermite-Hadamard type inequalities.

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.

scholarly journals Ostrowski Type Inequalities Pertaining Strongly Convex Functions Via Conformable Fractional Integrals and Their Applications

2019 ◽  
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integrals ◽  
Strongly Convex Functions ◽  
Strongly Convex Function ◽  
Strongly Convex ◽  
Error Estimations

In the article, by applied the concept of strongly convex function and one known identity, we establish several Ostrowski type inequalities involving conformable fractional integrals. As applications, some new error estimations for the midpoint formula are provided as well.

scholarly journals Inequalities Pertaining Fractional Approach through Exponentially Convex Functions

2019 ◽  
Vol 3 (3) ◽  
pp. 37 ◽  
Author(s):  
Saima Rashid ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integrals ◽  
Exponentially Convex Functions

In this article, certain Hermite-Hadamard-type inequalities are proven for an exponentially-convex function via Riemann-Liouville fractional integrals that generalize Hermite-Hadamard-type inequalities. These results have some relationships with the Hermite-Hadamard-type inequalities and related inequalities via Riemann-Liouville fractional integrals.

scholarly journals Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
M. Rostamian Delavar ◽  
S. Mohammadi Aslani ◽  
M. De La Sen
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integrals ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Absolute Value ◽  
Fejér Inequality ◽  
The Absolute

This paper deals with Hermite-Hadamard-Fejér inequality for (η1,η2)-convex functions via fractional integrals. Some mid-point and trapezoid type inequalities related to Hermite-Hadamard inequality when the absolute value of derivative of considered function is (η1,η2)-convex functions are obtained. Furthermore, a refinement for classic Hermite-Hadamard inequality via fractional integrals is given when a positive (η1,η2)-convex function is increasing.

scholarly journals Generalized fractional integral inequalities of Hermite-Hadamard-type for a convex function

2020 ◽  
Vol 18 (1) ◽  
pp. 794-806 ◽  
Author(s):  
Jiangfeng Han ◽  
Pshtiwan Othman Mohammed ◽  
Huidan Zeng
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Primary Objective ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Generalized Fractional Integral

Abstract The primary objective of this research is to establish the generalized fractional integral inequalities of Hermite-Hadamard-type for MT-convex functions and to explore some new Hermite-Hadamard-type inequalities in a form of Riemann-Liouville fractional integrals as well as classical integrals. It is worth mentioning that our work generalizes and extends the results appeared in the literature.

scholarly journals Hadamard and Fejér–Hadamard Inequalities for α , h − m − p -Convex Functions via Riemann–Liouville Fractional Integrals

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Wenyan Jia ◽  
Muhammad Yussouf ◽  
Ghulam Farid ◽  
Khuram Ali Khan
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Different Types ◽  
Hadamard Fractional Integral

In this paper, we introduce α , h − m − p -convex function and some related functions. By applying this generalized definition, new versions of Hadamard and Fejér–Hadamard fractional integral inequalities for Riemann–Liouville fractional integrals are given. The presented results hold at the same time for different types of convexities.

scholarly journals NEW INEQUALITIES OF OSTROWSKI TYPE FOR CO-ORDINATED CONVEX FUNCTIONS VIA GENERALIZED FRACTIONAL INTEGRALS

2021 ◽  
pp. 899
Author(s):  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Zhiyue Zhang
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
New Inequalities

In this paper, we establish new inequalities of Ostrowski type for co-ordinated convex function by using generalized fractional integral. We also discuss some special cases of our established results.

scholarly journals Some fractional Hermite–Hadamard-type integral inequalities with s-$(\alpha,m)$-convex functions and their applications

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
R. N. Liu ◽  
Run Xu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Second Order ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Special Means ◽  
Type Integral

AbstractUnder the new concept of s-$(\alpha,m)$ ( α , m ) -convex functions, we obtain some new Hermite–Hadamard inequalities with an s-$(\alpha,m)$ ( α , m ) -convex function. We use these inequalities to estimate Riemann–Liouville fractional integrals with second-order differentiable convex functions to enrich the Hermite–Hadamard-type inequalities. We give some applications to special means.

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