On generalizations related to the left side of Fejer's inequality via fractional integral operator

Set, Erhan; Çeli̇k, Bariş

doi:10.18514/mmn.2017.2275

Cited by 10 publications

(6 citation statements)

References 11 publications

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“…The significant extent of utilities of the integral inequalities on convexity for both derivation and integration has been a subject of hot debate. Set et al [25] illustrated numerous novel versions of Hermite-Hadamard-Fejér type inequalities via fractional integral operators.…”

Section: Introductionmentioning

confidence: 99%

New fractional approaches for n-polynomial P-convexity with applications in special function theory

et al. 2020

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Inequality theory provides a significant mechanism for managing symmetrical aspects in real-life circumstances. The renowned distinguishing feature of integral inequalities and fractional calculus has a solid possibility to regulate continuous issues with high proficiency. This manuscript contributes to a captivating association of fractional calculus, special functions and convex functions. The authors develop a novel approach for investigating a new class of convex functions which is known as an n-polynomial $\mathcal{P}$ P -convex function. Meanwhile, considering two identities via generalized fractional integrals, provide several generalizations of the Hermite–Hadamard and Ostrowski type inequalities by employing the better approaches of Hölder and power-mean inequalities. By this new strategy, using the concept of n-polynomial $\mathcal{P}$ P -convexity we can evaluate several other classes of n-polynomial harmonically convex, n-polynomial convex, classical harmonically convex and classical convex functions as particular cases. In order to investigate the efficiency and supremacy of the suggested scheme regarding the fractional calculus, special functions and n-polynomial $\mathcal{P}$ P -convexity, we present two applications for the modified Bessel function and $\mathfrak{q}$ q -digamma function. Finally, these outcomes can evaluate the possible symmetric roles of the criterion that express the real phenomena of the problem.

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Section: Introductionmentioning

confidence: 99%

New fractional approaches for n-polynomial P-convexity with applications in special function theory

et al. 2020

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“…Many famous inequalities can be obtained using the concept of convex functions. For details, interested readers are referred to [4][5][6][7][8][9][10][11][12][13][14]. Among these inequalities, Hermite-Hadamard's inequality, which provides us a necessary and sufficient condition for a function to be convex, is one of the most studied results.…”

Section: Introductionmentioning

confidence: 99%

On a new class of convex functions and integral inequalities

Awan

Noor

et al. 2019

J Inequal Appl

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“…This approach has opened a new path for research. Additionally, the authors of the manuscript [23,24] illustrated some important inequalities installed by Set et al Since then numerous scientists have broadly used the ideas of fractional calculus and received several new and novel refinements of inequalities via convex functions and their generalizations. Various papers with new indication, different speculations, and augmentations have appeared in the literature.…”

Section: Introductionmentioning

confidence: 99%

Fractional Integral Inequalities for Strongly h -Preinvex Functions for a kth Order Differentiable Functions

et al. 2019

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The objective of this paper is to derive Hermite-Hadamard type inequalities for several higher order strongly h -preinvex functions via Riemann-Liouville fractional integrals. These results are the generalizations of the several known classes of preinvex functions. An identity associated with k-times differentiable function has been established involving Riemann-Liouville fractional integral operator. A number of new results can be deduced as consequences for the suitable choices of the parameters h and σ . Our outcomes with these new generalizations have the abilities to be implemented for the evaluation of many mathematical problems related to real world applications.

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On generalizations related to the left side of Fejer's inequality via fractional integral operator

Cited by 10 publications

References 11 publications

New fractional approaches for n-polynomial P-convexity with applications in special function theory

New fractional approaches for n-polynomial P-convexity with applications in special function theory

On a new class of convex functions and integral inequalities

Fractional Integral Inequalities for Strongly h -Preinvex Functions for a kth Order Differentiable Functions

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