Hermite-Hadamard Type Inequalities for P-Convex Functions via Katugampola Fractional Integrals

Toplu, Tekin; Set, Erhan; Işcan, İ̇mdat; Maden, Selahattin

doi:10.22190/fumi1901149t

Cited by 10 publications

(11 citation statements)

References 16 publications

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“…Moreover, a midpoint-type identity for a function via another strictly monotone function is established, and corresponding inequalities are studied. The findings of this article are connected with the inequalities proved in [6,8,10,12,17,[20][21][22].…”

mentioning

confidence: 57%

“…The inequalities presented in this paper provide general formulas for fractional versions of trapezoidal and midpoint inequalities for strictly monotone functions. It is noted that the results presented in the published articles [6,8,10,12,17,[20][21][22] can be generated by considering the strictly monotone functions x, 1 x , x r , r = 0, and ln x. The readers can produce corresponding inequalities by taking other strictly monotone functions of their choice.…”

Section: Discussionmentioning

confidence: 99%

“…x , μ = 1, identity (2.1) provides Lemma 2.5 of [8]. By setting φ(x) = x r , identity (2.1) reduces to Lemma 2.1 for Riemann-Liouville fractional integrals of [22]; for φ(x) = x r , μ = 1, identity (2.1) provides Lemma 2.4 of [17]. By considering other strictly monotone functions in place of φ, many other corresponding identities can be formulated.…”

Section: Error Estimation Of Hermite-hadamard Inequality For a Convex...mentioning

confidence: 99%

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Inequalities for fractional Riemann–Liouville integrals of certain class of convex functions

2022

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Fractional calculus operators play a very important role in generalizing concepts of calculus used in diverse fields of science. In this paper, we use Riemann–Liouville fractional integrals to establish generalized identities, which are further applied to obtain midpoint and trapezoidal inequalities for convex function with respect to a strictly monotone function. These inequalities reproduce midpoint and trapezoidal inequalities for convex, harmonic convex, p-convex, and geometrically convex functions. Also, some new inequalities can be generated via specific strictly monotone functions.

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mentioning

confidence: 57%

Section: Discussionmentioning

confidence: 99%

Section: Error Estimation Of Hermite-hadamard Inequality For a Convex...mentioning

confidence: 99%

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Inequalities for fractional Riemann–Liouville integrals of certain class of convex functions

2022

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“…Since then, some improved and generalized results of Hermite-Hadamard inequality on convex function have been explored and study by many authors(e.g. [2], [7], [10][11][12], [20], [23,24], [27], [29]).…”

Section: Introductionmentioning

confidence: 99%

Some Hermite-Hadamard Type Inequalities via Katugampola Fractional for pq-Convex on the Interval-Valued Coordinates

Lo¹

2022

Int. J. Anal. Appl.

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“…Firstly, by using fractional integrals, Sarikaya et al [9] discovered fractional H-H inequality for classical convex function. After that, many scholars devoted their efforts to present fractional H-H type inequalities for different classes of convex and nonconvex functions see [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities

Sana¹,

Khan²,

Noor³

et al. 2021

IJCIS

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It is well known that the concept of convexity establishes strong relationship with integral inequality for single-valued and interval-valued function. The single-valued function and interval-valued function both are special cases of fuzzy interval-valued function. The aim of this paper is to introduce a new class of convex fuzzy interval-valued functions, which is called harmonically convex fuzzy interval-valued functions (harmonically convex fuzzy-IVFs) by means of fuzzy order relation and to investigate this new class via fuzzy-interval Riemann-Liouville fractional operator. With the help of fuzzy order relation and fuzzyinterval Riemann-Liouville fractional, we derive some integrals inequalities of Hermite-Hadamard (H-H) type and Hermite-Hadamard-Fejér (H-H Fejér) type as well as some product inequities for harmonically convex fuzzy-IVFs. Our results represent a significant improvement and refinement of the known results. We hope that these interesting outcomes may open a new direction for fuzzy optimization, modeling and interval-valued function.

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Hermite-Hadamard Type Inequalities for P-Convex Functions via Katugampola Fractional Integrals

Cited by 10 publications

References 16 publications

Inequalities for fractional Riemann–Liouville integrals of certain class of convex functions

Inequalities for fractional Riemann–Liouville integrals of certain class of convex functions

Some Hermite-Hadamard Type Inequalities via Katugampola Fractional for pq-Convex on the Interval-Valued Coordinates

Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities

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