Integral Inequalities for s-Convexity via Generalized Fractional Integrals on Fractal Sets

Almutairi, Ohud; Kılıçman, Adem

doi:10.3390/math8010053

Cited by 13 publications

(6 citation statements)

References 21 publications

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“…By means of the generalized m-convexity on fractal sets, Du et al [11] studied the Hermite-Hadamard-type, Hermite-Hadamard-Fejér-type and Simpson-type inequalities. Almutairi and Kilic ¸man [3,4] established certain Hermite-Hadamard type by means of generalized (h − m)-convexity as well as s-convexity, respectively. Iftikhar [14] presented several Newton's type inequalities by virtue of local fractional integrals.…”

Section: Introductionmentioning

confidence: 99%

Certain error bounds on the Bullen type integral inequalities in the framework of fractal spaces

2022

J. Nonlinear Funct. Anal.

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By virtue of Yang's fractal sets R ϖ (0 < ϖ ≤ 1), this paper is devoted to studying a number of integral inequalities, which are associate with the celebrated Bullen type inequality. To this end, an integral equality via local differentiable mappings is presented from which we obtain certain error estimations in connection with the Bullen type inequalities. Moreover, we provide three examples to identify the correctness of the outcomes. Considering the applications of the derived findings, we investigate several local fractional integral inequalities for ϖ-type special means, numerical integrations, and extended probability distribution mappings, respectively.

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Section: Introductionmentioning

confidence: 99%

Certain error bounds on the Bullen type integral inequalities in the framework of fractal spaces

2022

J. Nonlinear Funct. Anal.

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“…The H-H inequality plays essential roles in different areas of sciences, such as mathematics, physics and engineering (for example see [3,12,32,27,25]). This inequality provides estimates for the mean value of a continuous convex function.…”

Section: Introductionmentioning

confidence: 99%

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

Almutairi,

Kiliçman

2021

Preprint

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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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“…inequality for regular convex function was studied by [3]. Furthermore, many researchers have been studying the generalization of inequality in (1) motivated by various modifications of the notion of convexity, such as s-convexity and generalized s-convexity, for example see the details in ( [4][5][6][7]), where Hermite-Hadamard inequality were extended in order to include the problems that related to fractional calculus, a branch of calculus dealing with derivatives and integrals of non-integer order (see [8][9][10][11][12][13]). Nowadays, the real-life applications of fractional calculus exist in most areas of studies [14,15].…”

Section: Introductionmentioning

confidence: 99%

New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals

Almutairi

Kılıçman

2020

Symmetry

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In this paper, a new identity for the generalized fractional integral is defined. Using this identity we studied a new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. This fractional integral generalizes Riemann-Liouville and Hadamard’s integral, which possess a symmetric property. We derive trapezoid and mid-point type inequalities connected to this generalized Hermite-Hadamard inequality.

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Integral Inequalities for s-Convexity via Generalized Fractional Integrals on Fractal Sets

Cited by 13 publications

References 21 publications

Certain error bounds on the Bullen type integral inequalities in the framework of fractal spaces

Certain error bounds on the Bullen type integral inequalities in the framework of fractal spaces

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

New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals

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