New Hermite-Hadamard and Jensen Type Inequalities for h-Convex Functions on Fractal Sets

Vivas, Miguel; Hernández, Javier Domínguez; Merentes, Nelson

doi:10.15446/recolma.v50n2.62207

Cited by 33 publications

(21 citation statements)

References 14 publications

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“…Du et al [38] contemplated certain inequalities for generalized m-convex functions on fractal sets with utilities. 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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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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“…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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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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“…Vivas et al 36 proposed generalized h ‐convex function. And Sun 37 introduced another form of this definition with β ‐type.…”

Section: Introductionmentioning

confidence: 99%

“…Based on Yang's fractal theory, many scholars who are engaged in inequalities research also extend the research of inequalities to fractal sets. A series of definitions such as generalized convex function, 29,30 generalized harmonically convex functions, 31,32 generalized preinvex functions, 33,34 generalized m-convexity, 35 generalized h-convexity, 36,37 and generalized strongly m-convex 38 on fractal sets were introduced successively. And some inequalities for these types of functions were proposed, such as the literature.…”

Section: Introductionmentioning

confidence: 99%

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Some new inequalities for generalized h‐convex functions involving local fractional integral operators with Mittag‐Leffler kernel

Sun

2020

Math Methods in App Sciences

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In this paper, we firstly construct two local fractional integral operators with Mittag‐Leffler kernel on Yang's fractal sets. Then, two local fractional integral identities with the first‐ and second‐order derivatives are derived. With these as auxiliary tools, we establish some new Hermite‐Hadamard–type local fractional integral inequalities involving the local fractional integral operators with Mittag‐Leffler kernel for generalized h‐convex functions. In addition, we obtain some special inequalities when the parameter β and function h take special values. Finally, two examples are given to illustrate the application of the results.

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New Hermite-Hadamard and Jensen Type Inequalities for h-Convex Functions on Fractal Sets

Abstract: In this paper, some new Jensen and Hermite-Hadamard inequalities for h-convex functions on fractal sets are obtained. Results proved in this paper may stimulate further research in this area.

Cited by 33 publications

References 14 publications

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

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

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

Some new inequalities for generalized h‐convex functions involving local fractional integral operators with Mittag‐Leffler kernel

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