scholarly journals Hermite-Hadamard type inequalities for interval-valued exponential type pre-invex functions via Riemann-Liouville fractional integrals

2021 ◽  
Vol 7 (2) ◽  
pp. 2602-2617
Author(s):  
Hongling Zhou ◽  
◽  
Muhammad Shoaib Saleem ◽  
Waqas Nazeer ◽  
Ahsan Fareed Shah ◽  
...  
Keyword(s):  
Exponential Type ◽  
Fractional Integrals ◽  
Fractional Operator ◽  
Invex Functions ◽  
Interval Valued

<abstract><p>In the present research, we develop Hermite-Hadamard type inequalities for interval-valued exponential type pre-invex functions in Riemann-Liouville interval-valued fractional operator settings. Moreover, we develop He's inequality for interval-valued exponential type pre-invex functions.</p></abstract>

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.

A note on vanishing Morrey → VMO result for fractional integrals of variable order

2020 ◽  
Vol 23 (1) ◽  
pp. 298-302 ◽  
Author(s):  
Humberto Rafeiro ◽  
Stefan Samko
Keyword(s):  
Morrey Space ◽  
Morrey Spaces ◽  
Fractional Integrals ◽  
Variable Order ◽  
Fractional Operator ◽  
Limiting Case

AbstractIn the limiting case of Sobolev-Adams theorem for Morrey spaces of variable order we prove that the fractional operator of variable order maps the corresponding vanishing Morrey space into VMO.

scholarly journals On modified convex interval valued functions and related inclusions via the interval valued generalized fractional integrals in extended interval space

2021 ◽  
Vol 6 (5) ◽  
pp. 4638-4663
Author(s):  
Manar A. Alqudah ◽  
◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Muhammad Raees ◽  
...  
Keyword(s):  
Fractional Integrals ◽  
Interval Space ◽  
Interval Valued

scholarly journals Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 204
Author(s):  
Muhammad Bilal Khan ◽  
Hatim Ghazi Zaini ◽  
Savin Treanțǎ ◽  
Mohamed S. Soliman ◽  
Kamsing Nonlaopon
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Order Relation ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Invex Functions ◽  
Left And Right ◽  
Interval Valued

The concepts of convex and non-convex functions play a key role in the study of optimization. So, with the help of these ideas, some inequalities can also be established. Moreover, the principles of convexity and symmetry are inextricably linked. In the last two years, convexity and symmetry have emerged as a new field due to considerable association. In this paper, we study a new version of interval-valued functions (I-V·Fs), known as left and right χ-pre-invex interval-valued functions (LR-χ-pre-invex I-V·Fs). For this class of non-convex I-V·Fs, we derive numerous new dynamic inequalities interval Riemann–Liouville fractional integral operators. The applications of these repercussions are taken into account in a unique way. In addition, instructive instances are provided to aid our conclusions. Meanwhile, we’ll discuss a few specific examples that may be extrapolated from our primary findings.

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 Variable exponent fractional integrals in the limiting case α(x)p(n) ≡ n on quasimetric measure spaces

2020 ◽  
Vol 27 (1) ◽  
pp. 157-164
Author(s):  
Stefan Samko
Keyword(s):  
Growth Condition ◽  
Lebesgue Space ◽  
Measure Space ◽  
Variable Exponent ◽  
Fractional Integrals ◽  
Variable Order ◽  
Fractional Operator ◽  
Open Set ◽  
Measure Spaces ◽  
Limiting Case

AbstractWe show that the fractional operator {I^{\alpha(\,\cdot\,)}}, of variable order on a bounded open set in Ω, in a quasimetric measure space {(X,d,\mu)} in the case {\alpha(x)p(x)\equiv n} (where n comes from the growth condition on the measure μ), is bounded from the variable exponent Lebesgue space {L^{p(\,\cdot\,)}(\Omega)} into {\mathrm{BMO}(\Omega)} under certain assumptions on {p(x)} and {\alpha(x)}.

scholarly journals Certain Results Comprising the Weighted Chebyshev Function Using Pathway Fractional Integrals

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 896 ◽  
Author(s):  
Aditya Mani Mishra ◽  
Dumitru Baleanu ◽  
Fairouz Tchier ◽  
Sunil Dutt Purohit
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Chebyshev Inequality ◽  
Integral Parameter ◽  
Fractional Operator ◽  
Weighted Function ◽  
Fractional Integral Operators ◽  
Chebyshev Function

An analogous version of Chebyshev inequality, associated with the weighted function, has been established using the pathway fractional integral operators. The result is a generalization of the Chebyshev inequality in fractional integral operators. We deduce the left sided Riemann Liouville version and the Laplace version of the same identity. Our main deduction will provide noted results for an appropriate change to the Pathway fractional integral parameter and the degree of the fractional operator.

scholarly journals Some fractional Hermite–Hadamard-type inequalities for interval-valued coordinated functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Fangfang Shi ◽  
Guoju Ye ◽  
Dafang Zhao ◽  
Wei Liu
Keyword(s):  
Primary Objective ◽  
Fractional Integrals ◽  
Liouville Type ◽  
Interval Valued

AbstractThe primary objective of this paper is establishing new Hermite–Hadamard-type inequalities for interval-valued coordinated functions via Riemann–Liouville-type fractional integrals. Moreover, we obtain some fractional Hermite–Hadamard-type inequalities for the product of two coordinated h-convex interval-valued functions. Our results generalize several well-known inequalities.

scholarly journals Generalized fractional Hermite-Hadamard type inclusions for co-ordinated convex interval-valued functions

2020 ◽  
Author(s):  
Hasan KARA ◽  
Hüseyin BUDAK ◽  
Muhammad Aamir Ali
Keyword(s):  
Fractional Integrals ◽  
Functions Of Two Variables ◽  
Interval Valued

In this paper, we introduce the notion of generalized fractional integrals for the interval-valued functions of two variables. We establish Hermite-Hadamard type inequalities and some related inequalities for co-ordinated convex interval-valued functions by using the newly defined integrals. It is also proved that the results given in this paper are the strong generalization of already published ones.

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