On generalization of some inequalities for generalized harmonically convex functions via local fractional integrals

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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“…(3) If we take p = -1, then we get a definition given in [66]. (4) If we take p = 1 withα = 1, then we get the classical convex function.…”

Section: Main Results and Discussionmentioning

confidence: 99%

“…In addition to these results, Luo et al [62], deduced several new Fejér-Hermite-Hadamard inequalities for a class of h-convex functions with applications. For some useful and recent studies on fractional calculus and its applications in different fields of mathematics [63][64][65][66][67][68].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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“…Also, Vivas et al [44] explored generalized Jensen and HH inequalities for h-convex functions. For results associated with local fractional inequalities, we refer the interested readers to [24,[45][46][47] and the references therein.…”

Section: Lemma 18 ([43]mentioning

confidence: 99%

Some new local fractional inequalities associated with generalized $(s,m)$-convex functions and applications

et al. 2020

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Fractal analysis is one of interesting research areas of computer science and engineering, which depicts a precise description of phenomena in modeling. Visual beauty and self-similarity has made it an attractive field of research. The fractal sets are the effective tools to describe the accuracy of the inequalities for convex functions. In this paper, we employ linear fractals R α to investigate the (s, m)-convexity and relate them to derive generalized Hermite-Hadamard (HH) type inequalities and several other associated variants depending on an auxiliary result. Under this novel approach, we aim at establishing an analog with the help of local fractional integration. Meanwhile, we establish generalized Simpson-type inequalities for (s, m)-convex functions. The results in the frame of local fractional showed that among all comparisons, we can only see the correlation between novel strategies and the earlier consequences in generalized s-convex, generalized m-convex, and generalized convex functions. We obtain application in probability density functions and generalized special means to confirm the relevance and computational effectiveness of the considered method. Similar results in this dynamic field can also be widely applied to other types of fractals and explored similarly to what has been done in this paper.

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“…It has been applied to differential equations and other fields . Many researchers began to study the Hermite‐Hadamard type inequalities on Yang's fractal sets, and achieved some new results . Mo et al in introduced generalized convex function and generalized

s

‐convex function on Yang's fractal sets, respectively.…”

Section: Introductionmentioning

confidence: 99%

Hadamard type local fractional integral inequalities for generalized harmonically convex functions and applications

Sun

Liu

2020

Math Methods in App Sciences

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In this paper, we establish a local fractional integral identity with a parameter λ on Yang's fractal sets. Using this identity, by generalized power mean inequality and generalized Hölder inequality, two Hermite‐Hadamard type local fractional integral inequalities for generalized harmonically convex functions are established. By giving some special values to the parameter, some inequalities with specific form can be obtained. Some applications to generalized special means are given.

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On generalization of some inequalities for generalized harmonically convex functions via local fractional integrals

Cited by 38 publications

References 18 publications

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

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

Some new local fractional inequalities associated with generalized $(s,m)$-convex functions and applications

Hadamard type local fractional integral inequalities for generalized harmonically convex functions and applications

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