scholarly journals On Hermite-Hadamard-Fejér type integral inequalities for generalized convex functions via local fractional integrals

2019 ◽  
Vol 3 (1) ◽  
pp. 273-284 ◽  
Author(s):  
Mehmet Zeki Sarikaya ◽  
◽  
Necmettin Alp ◽  
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Generalized Convex Functions ◽  
Type Integral

scholarly journals SIMPSON’S TYPE INEQUALITIES VIA THE KATUGAMPOLA FRACTIONAL INTEGRALS FOR s-CONVEX FUNCTIONS

2021 ◽  
Vol 45 (5) ◽  
pp. 709-720
Author(s):  
SETH KERMAUSUOR ◽  
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Type Integral ◽  
Hadamard Fractional Integrals

In this paper, we introduce some Simpson’s type integral inequalities via the Katugampola fractional integrals for functions whose first derivatives at certain powers are s-convex (in the second sense). The Katugampola fractional integrals are generalizations of the Riemann–Liouville and Hadamard fractional integrals. Hence, our results generalize some results in the literature related to the Riemann–Liouville fractional integrals. Results related to the Hadamard fractional integrals could also be derived from our results.

scholarly journals Hermite-Hadamard type inequalities for p-convex functions via fractional integrals

2017 ◽  
Vol 3 (1) ◽  
pp. 22-34 ◽  
Author(s):  
Mehmet Kunt ◽  
İmdat İşcan
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Integral Forms ◽  
Type Integral ◽  
Integral Equality

Abstract In this paper, we present Hermite-Hadamard inequality for p-convex functions in fractional integral forms. we obtain an integral equality and some Hermite-Hadamard type integral inequalities for p-convex functions in fractional integral forms. We give some Hermite-Hadamard type inequalities for convex, harmonically convex and p-convex functions. Some results presented in this paper for p-convex functions, provide extensions of others given in earlier works for convex, harmonically convex and p-convex functions.

scholarly journals Hermite-Hadamard-Fejér Type Inequalities for Quasi-Geometrically Convex Functions via Fractional Integrals

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
İmdat İşcan ◽  
Mehmet Kunt
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Integral Forms ◽  
Type Integral

Some Hermite-Hadamard-Fejér type integral inequalities for quasi-geometrically convex functions in fractional integral forms have been obtained.

scholarly journals Simpson’s type inequalities for η-convex functions via k-Riemann–Liouville fractional integrals

2020 ◽  
Vol 23 (2) ◽  
pp. 193-200
Author(s):  
Seth Kermausuor
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Type Integral

We introduce some Simpson's type integral inequalities via k-Riemann–Liouville fractional integrals for functions whose derivatives are η-convex. These results generalize some results in the literature.

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>

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.

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.

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