Improvement of some inequalities of Chebysev–Grüss type

Gavrea, Bogdan

doi:10.1016/j.camwa.2012.03.101

Cited by 8 publications

(3 citation statements)

References 4 publications

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“…Therefore, several generalizations of this type of integral inequality have been extensively addressed by researchers (see, e.g., [16], [20], [21], [22], [25], [26], [29], [34], [35], [36], [39], [40], [41], [49]). Moreover, by applying fractional integral operators and fractional q-integral operators, many authors have obtained a lot of fractional integral inequalities, their q-analogues and applications (see, e.g., [7], [11], [12], [13], [14], [17], [28], [38], [42], [43], [51], and the references cited therein).…”

Section: Introductionmentioning

confidence: 99%

A Grüss Type Integral Inequality Associated With Gauss Hypergeometric Function Fractional Integral Operator

Choi¹,

Purohıt²

2015

Communications of the Korean Mathematical Society

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Section: Introductionmentioning

confidence: 99%

A Grüss Type Integral Inequality Associated With Gauss Hypergeometric Function Fractional Integral Operator

Choi¹,

Purohıt²

2015

Communications of the Korean Mathematical Society

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“…This inequality has been studied and generalized by several authors; see [5][6][7]. In [7], the term Chebyshev-Grüss inequalities is used mentioning to Grüss inequalities for Chebyshev functions T I which defined as…”

Section: Introductionmentioning

confidence: 99%

Integral Inequalities of Chebyshev Type for Continuous Fields of Hermitian Operators Involving Tracy–Singh Products and Weighted Pythagorean Means

Ploymukda

Chansangiam

2019

Symmetry

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In this paper, we establish several integral inequalities of Chebyshev type for bounded continuous fields of Hermitian operators concerning Tracy-Singh products and weighted Pythagorean means. The weighted Pythagorean means considered here are parametrization versions of three symmetric means: the arithmetic mean, the geometric mean, and the harmonic mean. Every continuous field considered here is parametrized by a locally compact Hausdorff space equipped with a finite Radon measure. Tracy-Singh product versions of the Chebyshev-Grüss inequality via oscillations are also obtained. Such integral inequalities reduce to discrete inequalities when the space is a finite space equipped with the counting measure. Moreover, our results include Chebyshev-type inequalities for tensor product of operators and Tracy-Singh/Kronecker products of matrices.

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“…Therefore, in the literature we found several extensions and generalizations of these integral inequalities for the functions of bounded variation, synchronous, Lipschitzian, monotonic, absolutely continuous and n-times differentiable mappings etc. ( [10,11,12,15,16,19,20,21,22,26,27,28]). In the past recent years, one more dimension have been added to this study, by introducing number of integral inequalities involving various fractional calculus and qcalculus operators.…”

Section: Introductionmentioning

confidence: 99%