scholarly journals New Riemann–Liouville fractional Hermite–Hadamard type inequalities for harmonically convex functions

2019 ◽  
Vol 9 (2) ◽  
pp. 431-441
Author(s):  
Zeynep Şanlı ◽  
Mehmet Kunt ◽  
Tuncay Köroğlu
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Differentiable Functions ◽  
Left And Right ◽  
Harmonically Convex Functions

Abstract In this paper, we proved two new Riemann–Liouville fractional Hermite–Hadamard type inequalities for harmonically convex functions using the left and right fractional integrals independently. Also, we have two new Riemann–Liouville fractional trapezoidal type identities for differentiable functions. Using these identities, we obtained some new trapezoidal type inequalities for harmonically convex functions. Our results generalize the results given by İşcan (Hacet J Math Stat 46(6):935–942, 2014).

scholarly journals Bounds of Riemann-Liouville Fractional Integrals in General Form via Convex Functions and Their Applications

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 248 ◽  
Author(s):  
Ghulam Farid ◽  
Waqas Nazeer ◽  
Muhammad Saleem ◽  
Sajid Mehmood ◽  
Shin Kang
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Novel Approach ◽  
Left And Right

In this article, we establish bounds of sum of the left and right sided Riemann Liouville (RL) fractional integrals and related inequalities in general form. A new and novel approach is followed to obtain these results for general Riemann Liouville (RL) fractional integrals. Monotonicity and convexity of functions are used with some usual and straight forward inequalities. The presented results are also have connection with some known and already published results. Applications and motivations of presented results are briefly discussed.

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 Hermite-Hadamard-Fejér type inequalities for co-ordinated harmonically convex functions via Katugampola fractional integrals

2021 ◽  
Vol 4 (2) ◽  
pp. 12-28
Author(s):  
Naila Mehreen ◽  
◽  
Matloob Anwar ◽  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
One Dimension ◽  
Harmonically Convex Functions ◽  
Katugampola Fractional Integral

The aim of this paper is to establish the Hermite-Hadamard-Fejér type inequalities for co-ordinated harmonically convex functions via Katugampola fractional integral. We provide Hermite-Hadamard-Fejér inequalities for harmonically convex functions via Katugampola fractional integral in one dimension.

scholarly journals Hadamard and Fejér–Hadamard Inequalities for Further Generalized Fractional Integrals Involving Mittag-Leffler Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
M. Yussouf ◽  
G. Farid ◽  
K. A. Khan ◽  
Chahn Yong Jung
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Harmonically Convex Functions

In this paper, generalized versions of Hadamard and Fejér–Hadamard type fractional integral inequalities are obtained. By using generalized fractional integrals containing Mittag-Leffler functions, some well-known results for convex and harmonically convex functions are generalized. The results of this paper are connected with various published fractional integral inequalities.

scholarly journals Bounds of Generalized Proportional Fractional Integrals in General Form via Convex Functions and Their Applications

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 113 ◽  
Author(s):  
Gauhar Rahman ◽  
Thabet Abdeljawad ◽  
Fahd Jarad ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Convex Functions ◽  
General Type ◽  
Fractional Integrals ◽  
New Approach ◽  
Left And Right ◽  
New Inequalities

In this paper, our objective is to apply a new approach to establish bounds of sums of left and right proportional fractional integrals of a general type and obtain some related inequalities. From the obtained results, we deduce some new inequalities for classical generalized proportional fractional integrals as corollaries. These inequalities have a connection with some known and existing inequalities which are mentioned in the literature. In addition, some applications of the main results are presented.

scholarly journals Extensions of Hermite–Hadamard inequalities for harmonically convex functions via generalized fractional integrals

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xue-Xiao You ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Praveen Agarwal ◽  
Yu-Ming Chu
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Convexity Property ◽  
Hadamard Inequality ◽  
Harmonically Convex Functions ◽  
Harmonic Convexity

AbstractIn the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite–Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.

scholarly journals Some integral inequalities for co-ordinated harmonically convex functions via fractional integrals

2020 ◽  
Vol 3 (4) ◽  
pp. 60-74
Author(s):  
Naila Mehreen ◽  
◽  
Matloob Anwar ◽  
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Harmonically Convex Functions

In this paper, we find some Hermite-Hadamard type inequalities for co-ordinated harmonically convex functions via fractional integrals.

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