Generalized Integral Inequalities for Hermite–Hadamard-Type Inequalities via s-Convexity on Fractal Sets

Almutairi, Ohud; Kılıçman, Adem

doi:10.3390/math7111065

Cited by 10 publications

(5 citation statements)

References 19 publications

(20 reference statements)

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“…The theory of convexity, moreover, is accepted as a critical part in the progression of the idea of inequalities. Inequalities have an intriguing mathematical model because of their significant applications in traditional calculus, fractional calculus [4], quantum calculus [5], interval valued [6], stochastic [7], time-scale calculus [8], fractal sets [9], etc. Definition 1 ([10]).…”

Section: Introductionmentioning

confidence: 99%

Some Novel Fractional Integral Inequalities over a New Class of Generalized Convex Function

et al. 2022

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The comprehension of inequalities in convexity is very important for fractional calculus and its effectiveness in many applied sciences. In this article, we handle a novel investigation that depends on the Hermite–Hadamard-type inequalities concerning a monotonic increasing function. The proposed methodology deals with a new class of convexity and related integral and fractional inequalities. There exists a solid connection between fractional operators and convexity because of its fascinating nature in the numerical sciences. Some special cases have also been discussed, and several already-known inequalities have been recaptured to behave well. Some applications related to special means, q-digamma, modified Bessel functions, and matrices are discussed as well. The aftereffects of the plan show that the methodology can be applied directly and is computationally easy to understand and exact. We believe our findings generalise some well-known results in the literature on s-convexity.

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Section: Introductionmentioning

confidence: 99%

Some Novel Fractional Integral Inequalities over a New Class of Generalized Convex Function

et al. 2022

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“…In recent years, many authors (see [7][8][9][10][11][12][13][14][15][16][17][18] and references therein) studied Hermite-Hadamardtype inequalities for improvements and generalizations. In these papers, new inequalities for functions from various convexity classes were obtained.…”

Section: Introductionmentioning

confidence: 99%

Generalization of Hadamard-type trapezoid inequalities for fractional integral operators

Bayraktar

Özdemi̇r

2021

Ufimsk. Mat. Zh.

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The role of convexity theory in applied problems, especially in optimization problems, is well known. The integral Hermite-Hadamard inequality has a special place in this theory since it provides an upper bound for the mean value of a function. In solving applied problems from different fields of science and technology, along with the classical integro-differential calculus, fractional calculus plays an important role. A lot of research is devoted to obtaining an upper bound in the Hermite-Hadamard inequality using operators of fractional calculus.The article formulates and proves the identity with the participation of the fractional integration operator. Based on this identity, new generalized Hadamard-type integral inequalities are obtained for functions for which the second derivatives are convex and take values at intermediate points of the integration interval. These results are obtained using the convexity property of a function and two classical integral inequalities, the Hermite-Hadamard integral inequality and its other form, the power mean inequality. It is shown that the upper limit of the absolute error of inequality decreases in approximately 2 times, where is the number of intermediate points. In a particular case, the obtained estimates are consistent with known estimates in the literature. The results obtained in the article can be used in further researches in the integro-differential fractional calculus.

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“…Due to the enormous importance of inequalities ( 1) and ( 2), many generalizations of such inequalities involving a variant types of convexities have been investigated [13,19,15,17]. For more interesting results, one can consult the following references [20,14,9,18,5].…”

Section: Introductionmentioning

confidence: 99%

Generalized Fejér-Hermite-Hadamard type via generalized $(h-m)$-convexity on fractal sets and applications

Almutairi,

Kiliçman

2021

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In this article, we define a new class of convexity called generalized (h − m)-convexity, which generalizes h-convexity and m-convexity on fractal set R α (0 < α ≤ 1). Some properties of this new class are discussed. Using local fractional integrals and generalized (h − m)-convexity, we generalized Hermite-Hadamard (H-H) and Fejér-Hermite-Hadamard (Fejér-H-H) types inequalities. We also obtained a new result of the Fejér-H-H type for the function whose derivative in absolute value is the generalized (h − m)-convexity on fractal sets. As applications, we studied some new inequalities for random variables and numerical integrations.

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Generalized Integral Inequalities for Hermite–Hadamard-Type Inequalities via s-Convexity on Fractal Sets

Cited by 10 publications

References 19 publications

Some Novel Fractional Integral Inequalities over a New Class of Generalized Convex Function

Some Novel Fractional Integral Inequalities over a New Class of Generalized Convex Function

Generalization of Hadamard-type trapezoid inequalities for fractional integral operators

Generalized Fejér-Hermite-Hadamard type via generalized $(h-m)$-convexity on fractal sets and applications

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