Generalized trapezoidal type integral inequalities and their applications

Kashuri, Artion; Liko, Rozana

doi:10.1007/s41478-020-00232-2

Cited by 7 publications

(4 citation statements)

References 17 publications

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“…Budak et al [12] proved several variants of Ostrowski's and Simpson's type for differentiable convex functions via generalized fractional integrals. For more inequalities via fractional integrals, one can consult [13][14][15][16][17][18][19][20][21][22][23][24] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Some Generalized Fractional Integral Inequalities for Convex Functions with Applications

et al. 2022

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In this paper, we establish a generalized fractional integrals identity involving some parameters and differentiable functions. Then, we use the newly established identity and prove different generalized fractional integrals inequalities like midpoint inequalities, trapezoidal inequalities and Simpson’s inequalities for differentiable convex functions. Finally, we give some applications of newly established inequalities in the context of quadrature formulas.

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Section: Introductionmentioning

confidence: 99%

Some Generalized Fractional Integral Inequalities for Convex Functions with Applications

et al. 2022

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“…On the other hand, there are many other papers related to our topic. One can consult [14][15][16][17][18][19][20][21][22][23][24][25] and references therein for more inequalities via fractional integrals. Moreover, several papers focused on the functions of bounded variation to prove some important inequalities such as the Ostrowski type [26], Simpson type [27,28], trapezoid type [29,30], and midpoint type [31].…”

Section: Introductionmentioning

confidence: 99%

Some New Generalized Fractional Newton’s Type Inequalities for Convex Functions

Soontharanon

Ali

Budak

et al. 2022

Journal of Function Spaces

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In this paper, we establish some new Newton’s type inequalities for differentiable convex functions using the generalized Riemann-Liouville fractional integrals. The main edge of the newly established inequalities is that these can be turned into several new and existing inequalities for different fractional integrals like Riemann-Liouville fractional integrals, k -fractional integrals, Katugampola fractional operators, conformable fractional operators, Hadamard fractional operators, and fractional operators with the exponential kernel without proving one by one. It is also shown that the newly established inequalities are the refinements of the previously established inequalities inside the literature.

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“…The basic structures of this theory are convex sets and convex functions, which play a crucial role in the advancement and applications of it in various branches of applied and pure mathematics 1–7 . Due to the widespread use of convexity in modern analysis, the notion of convex functions has been extended and generalized in several directions 8–19 . Some of these generalizations modify the domain or range of the function while preserving the basic structure of a convex function as it is defined in Peajcariaac and Tong 20 as follows:…”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7] Due to the widespread use of convexity in modern analysis, the notion of convex functions has been extended and generalized in several directions. [8][9][10][11][12][13][14][15][16][17][18][19] Some of these generalizations modify the domain or range of the function while preserving the basic structure of a convex function as it is defined in Peajcariaac and Tong 20…”

Section: Introductionmentioning

confidence: 99%

Some Hermite–Hadamard type inequalities for GA‐s‐convex functions in the fourth sense

Baidar

Kunt

2022

Math Methods in App Sciences

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In the present manuscript, we define the concept of GA$$ GA $$‐ s$$ s $$‐convex functions in the fourth sense. We obtain the Hermite–Hadamard inequality for the newly introduced class of functions. We also establish some inequalities of the Hermite–Hadamard type for functions whose first derivative in absolute value at certain powers is a GA$$ GA $$‐ s$$ s $$‐convex function in the fourth sense. In the last, some applications to special means of real numbers are given.

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Generalized trapezoidal type integral inequalities and their applications

Cited by 7 publications

References 17 publications

Some Generalized Fractional Integral Inequalities for Convex Functions with Applications

Some Generalized Fractional Integral Inequalities for Convex Functions with Applications

Some New Generalized Fractional Newton’s Type Inequalities for Convex Functions

Some Hermite–Hadamard type inequalities for GA‐s‐convex functions in the fourth sense

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