New extensions of Chebyshev-P&amp;#243;lya-Szeg&amp;#246; type inequalities via conformable integrals

Deni̇z, Erhan; Akdemir, Ahmet Ocak; Yüksel, Ebru

doi:10.3934/math.2020066

Cited by 8 publications

(6 citation statements)

References 7 publications

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“…The Hadamard inequality, which is well known in the field of fractional integrals, is the most celebrated inequality that has been studied for fractional integrals. Now, we give the definition of the conformable fractional derivative with its important properties, which are useful in order to obtain our main results, we suggest [9][10][11][12][13][14][15][16][17] for articles that deal with fractional integral inequalities using various forms of fractional integral operators to solve them.…”

Section: Fractional Calculusmentioning

confidence: 99%

Hermite-Hadamard-Fejér Type Inequalities with Generalized K-Fractional Conformable Integrals and Their Applications

Kalsoom

Khan

2022

Mathematics

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In this work, we introduce new definitions of left and right-sides generalized conformable K-fractional derivatives and integrals. We also prove new identities associated with the left and right-sides of the Hermite-Hadamard-Fejér type inequality for ϕ-preinvex functions. Moreover, we use these new identities to prove some bounds for the Hermite-Hadamard-Fejér type inequality for generalized conformable K-fractional integrals regarding ϕ-preinvex functions. Finally, we also present some applications of the generalized definitions for higher moments of continuous random variables, special means, and solutions of the homogeneous linear Cauchy-Euler and homogeneous linear K-fractional differential equations to show our new approach.

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Section: Fractional Calculusmentioning

confidence: 99%

Hermite-Hadamard-Fejér Type Inequalities with Generalized K-Fractional Conformable Integrals and Their Applications

Kalsoom

Khan

2022

Mathematics

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“…The well-known Pólya-Szegö inequality gives the estimation of quotient in terms of the Chebyshev inequality for bounded functions. These inequalities have been studied for Riemann-Liouville and other fractional integral operators in [10,[14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Generalized k-Fractional Integral Operators Associated with Pólya-Szegö and Chebyshev Types Inequalities

Zhang

Farid

Mehmood³

et al. 2022

Fractal Fract

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Inequalities related to derivatives and integrals are generalized and extended via fractional order integral and derivative operators. The present paper aims to define an operator containing Mittag-Leffler function in its kernel that leads to deduce many already existing well-known operators. By using this generalized operator, some well-known inequalities are studied. The results of this paper reproduce Chebyshev and Pólya-Szegö type inequalities for Riemann-Liouville and many other fractional integral operators.

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“…Integral operators play a very important role in the field of mathematical inequalities. A large number of integral inequalities exist in the literature for different types of integral operators [1][2][3][4][5][6][7][8][9]. Due to the extensions and generalizations of integral operators, it becomes possible to obtain extensions and generalizations of classical inequalities.…”

Section: Introductionmentioning

confidence: 99%

Generalized k-Fractional Chebyshev-Type Inequalities via Mittag-Leffler Functions

Zhang

Farid

Mehmood³

et al. 2022

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Mathematical inequalities have gained importance and popularity due to the application of integral operators of different types. The present paper aims to give Chebyshev-type inequalities for generalized k-integral operators involving the Mittag-Leffler function in kernels. Several new results can be deduced for different integral operators, along with Riemann–Liouville fractional integrals by substituting convenient parameters. Moreover, the presented results generalize several already published inequalities.

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New extensions of Chebyshev-Pólya-Szegö type inequalities via conformable integrals

Cited by 8 publications

References 7 publications

Hermite-Hadamard-Fejér Type Inequalities with Generalized K-Fractional Conformable Integrals and Their Applications

Hermite-Hadamard-Fejér Type Inequalities with Generalized K-Fractional Conformable Integrals and Their Applications

Generalized k-Fractional Integral Operators Associated with Pólya-Szegö and Chebyshev Types Inequalities

Generalized k-Fractional Chebyshev-Type Inequalities via Mittag-Leffler Functions

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