A sharp double inequality involving generalized complete elliptic integral of the first kind

Zhao, Tie-Hong; Wang, Miao-Kun; Chu, Yu‐Ming

doi:10.3934/math.2020290

Cited by 194 publications

(41 citation statements)

References 33 publications

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“…The fractional integral inequality [16][17][18][19][20][21][22][23][24] is one of the most popular approaches which is widely employed in many practical problems, optimization theory, engineering and technology. Integral inequalities of fractional strategies show substantially more ordinarily in several research areas and technology applications.…”

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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“…With the development of the inequality theory, the inequalities for various kinds of convex functions have a rapid blossom in the area of pure and applied mathematics [30][31][32][33][34][35][36][37][38][39][40][41][42]. As mentioned above, many articles are all involved with Hermite-Hadamard type and trapezoid type, midpoint type inequalities [43][44][45][46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

Some new Simpson-type inequalities for generalized p-convex function on fractal sets with applications

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The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish the generalization of Simpson-type inequalities for the class of functions whose local fractional derivatives in absolute values at certain powers are p-convex. The method we present is an alternative in showing the classical variants associated with generalized p-convex functions. Some parts of our results cover the classical convex functions and classical harmonically convex functions. Some novel applications in random variables, cumulative distribution functions and generalized bivariate means are obtained to ensure the correctness of the present results. The present approach is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractals in computer graphics.

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“…Many new integral inequalities and bounds to known inequalities have been found by using new integral operators. The new trends, improvements, and advances on fractional calculus and real world applications can be found in the literature [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. Now let us remember some integral operators that are well known to be useful in fractional analysis.…”

Section: Introductionmentioning

confidence: 99%

New Hermite–Jensen–Mercer-type inequalities via k-fractional integrals

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A sharp double inequality involving generalized complete elliptic integral of the first kind

Cited by 194 publications

References 33 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

Some new Simpson-type inequalities for generalized p-convex function on fractal sets with applications

New Hermite–Jensen–Mercer-type inequalities via k-fractional integrals

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