Some New Fractional Trapezium-Type Inequalities for Preinvex Functions

Kashuri, Artion; Set, Erhan; Liko, Rozana

doi:10.3390/fractalfract3010012

Cited by 8 publications

(2 citation statements)

References 23 publications

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“…We note that HermiteHadamard inequality may be regarded as a renement of the concept of convexity and it follows easily from Jensen's inequality. HermiteHadamard inequality for convex functions has received renewed attention in recent years and a remarkable variety of renements and generalizations have been studied, see [2,4,5,6,7,8,11,12,13,15,16,17,18,30].…”

Section: Introductionmentioning

confidence: 99%

SOME NEW TYPE INTEGRAL INEQUALITIES FOR APPROXIMATELY HARMONIC h-CONVEX FUNCTIONS

Meftah¹

2020

matbil

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In this paper, we present a new denition of preinvex functions depending on the given function which is called as approximately harmonic h-preinvex functions. We establish some inequalities of HermiteHadamard, Simpson and midpoint type for newly dene class of functions. We show that this class contains several other new and known extensions of harmonic preinvexity. Special cases which can be deduced from the main results are also discussed in detail.

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Section: Introductionmentioning

confidence: 99%

SOME NEW TYPE INTEGRAL INEQUALITIES FOR APPROXIMATELY HARMONIC h-CONVEX FUNCTIONS

Meftah¹

2020

matbil

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“…In recent years, several papers have been devoted to obtaining inequalities for generalized fractional integrals; for some of them please refer to [39][40][41][42][43][44][45].…”

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confidence: 99%

Some New Simpson’s-Formula-Type Inequalities for Twice-Differentiable Convex Functions via Generalized Fractional Operators

et al. 2021

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From the past to the present, various works have been dedicated to Simpson’s inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. In this paper, we establish a new generalized fractional integral identity involving twice-differentiable functions, then we use this result to prove some new Simpson’s-formula-type inequalities for twice-differentiable convex functions. Furthermore, we examine a few special cases of newly established inequalities and obtain several new and old Simpson’s-formula-type inequalities. These types of analytic inequalities, as well as the methodologies for solving them, have applications in a wide range of fields where symmetry is crucial.

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Generalized trapezoidal type integral inequalities and their applications

Kashuri

Liko

2020

J Anal

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Some New Fractional Trapezium-Type Inequalities for Preinvex Functions

Cited by 8 publications

References 23 publications

SOME NEW TYPE INTEGRAL INEQUALITIES FOR APPROXIMATELY HARMONIC h-CONVEX FUNCTIONS

SOME NEW TYPE INTEGRAL INEQUALITIES FOR APPROXIMATELY HARMONIC h-CONVEX FUNCTIONS

Some New Simpson’s-Formula-Type Inequalities for Twice-Differentiable Convex Functions via Generalized Fractional Operators

Generalized trapezoidal type integral inequalities and their applications

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