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

2020 ◽  
Vol 2020 (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.

scholarly journals Fractional Ostrowski type inequalities for differentiable harmonically convex functions

2021 ◽  
Vol 7 (3) ◽  
pp. 3939-3958
Author(s):  
Thanin Sitthiwirattham ◽  
◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Sotiris K. Ntouyas ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Special Means ◽  
Special Cases ◽  
Harmonically Convex Functions ◽  
New Inequalities

<abstract><p>In this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and $ k $-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities.</p></abstract>

scholarly journals New Inequalities for Strongly r-Convex Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Huriye Kadakal
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Special Cases ◽  
Class Of Functions ◽  
New Inequalities

In this study, firstly we introduce a new concept called “strongly r-convex function.” After that we establish Hermite-Hadamard-like inequalities for this class of functions. Moreover, by using an integral identity together with some well known integral inequalities, we establish several new inequalities for n-times differentiable strongly r-convex functions. In special cases, the results obtained coincide with the well-known results in the literature.

scholarly journals Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 534
Author(s):  
Fangfang Shi ◽  
Guoju Ye ◽  
Dafang Zhao ◽  
Wei Liu
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Liouville Type ◽  
Special Cases ◽  
The Relationship ◽  
Interval Valued

In this paper, firstly we prove the relationship between interval h-convex functions and interval harmonically h-convex functions. Secondly, several new Hermite–Hadamard type inequalities for interval h-convex functions via interval Riemann–Liouville type fractional integrals are established. Finally, we obtain some new fractional Hadamard–Hermite type inequalities for interval harmonically h-convex functions by using the above relationship. Also we discuss the importance of our results and some special cases. Our results extend and improve some previously known results.

scholarly journals New inequalities for F-convex functions pertaining generalized fractional integrals

2020 ◽  
Vol 24 (2) ◽  
pp. 117-131
Author(s):  
Hüseyın Budak ◽  
Pınar Kösem ◽  
Artion Kashuri
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Special Cases ◽  
New Inequalities

In this paper, the authors, utilizing F-convex functions which are defined by B. Samet, establish some new Hermite-Hadamard type inequalities via generalized fractional integrals. Some special cases of our main results recaptured the well-known earlier works.

scholarly journals Some New Hermite-Hadamard-Fejér Fractional Type Inequalities for h-Convex and Harmonically h-Convex Interval-Valued Functions

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 74
Author(s):  
Humaira Kalsoom ◽  
Muhammad Amer Latif ◽  
Zareen A. Khan ◽  
Miguel Vivas-Cortez
Keyword(s):  
Type Inequality ◽  
Fractional Integrals ◽  
Additional Observation ◽  
Additional Function ◽  
New Class ◽  
Special Cases ◽  
Definition Of ◽  
Interval Valued ◽  
Fractional Type

In this article, firstly, we establish a novel definition of weighted interval-valued fractional integrals of a function Υ˘ using an another function ϑ(ζ˙). As an additional observation, it is noted that the new class of weighted interval-valued fractional integrals of a function Υ˘ by employing an additional function ϑ(ζ˙) characterizes a variety of new classes as special cases, which is a generalization of the previous class. Secondly, we prove a new version of the Hermite-Hadamard-Fejér type inequality for h-convex interval-valued functions using weighted interval-valued fractional integrals of a function Υ˘ according to another function ϑ(ζ˙). Finally, by using weighted interval-valued fractional integrals of a function Υ˘ according to another function ϑ(ζ˙), we are establishing a new Hermite-Hadamard-Fejér type inequality for harmonically h-convex interval-valued functions that is not previously known. Moreover, some examples are provided to demonstrate our results.

scholarly journals Generalized fractional midpoint type inequalities for co-ordinated convex functions

2021 ◽  
Author(s):  
Fatih HEZENCİ ◽  
Hüseyin BUDAK ◽  
Hasan KARA ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Convex Functions ◽  
Research Paper ◽  
Fractional Integrals ◽  
Special Cases ◽  
Riemann Integrals ◽  
New Inequalities ◽  
Differentiable Mappings

In this research paper, we investigate generalized fractional integrals to obtain midpoint type inequalities for the co-ordinated convex functions. First of all, we establish an identity for twice partially differentiable mappings. By utilizing this equality, some midpoint type inequalities via generalized fractional integrals are proved. We also show that the main results reduce some midpoint inequalities given in earlier works for Riemann integrals and Riemann-Liouville fractional integrals. Finally, some new inequalities for $k$-Riemann-Liouville fractional integrals are presented as special cases of our results.

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 Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications

2021 ◽  
Vol 5 (3) ◽  
pp. 80
Author(s):  
Hari Mohan Srivastava ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Dumitru Baleanu ◽  
Y. S. Hamed
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Wright Function ◽  
Nonconvex Functions ◽  
Special Cases ◽  
Type Integral ◽  
Generic Class ◽  
Two Parameters ◽  
Class Of Functions

In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.

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

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.

Some Hermite-Hadamard type inequalities for convex functions via conformable fractional integrals and related inequalities

2017 ◽  
Vol 26 (2) ◽  
pp. 221-229
Author(s):  
ERHAN SET ◽  
MEHMET ZEKI SARIKAYA ◽  
ABDURRAHMAN GOZPINAR
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
The Given

In this present study, firstly we give some necessary definitions and some results related to Riemann-Liouville fractional and conformable fractional integrals. Secondly, using the given definitions , we established a new identity and Hermite-Hadamard type inequalities via conformable fractional integrals. Relevant connections of the results presented here with those earlier ones are also pointed out.

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