Some new bounds for Simpson's rule involving special functions via harmonic h-convexity

A new class of harmonic convex function depending on given functions which is called as "approximately harmonic h-convex functions" is introduced. With the discussion of special cases it is shown that this class unifies other classes of approximately harmonic h-convex function. Some associated integral inequalities with these new classes of harmonic convexity are also obtained. Several special cases of the main results are also discussed.

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“…Many famous inequalities are direct consequences of classical convexity. For more details see [1,2,6,[9][10][11]. Recently Noor at al.…”

Section: Introductionmentioning

confidence: 99%

On approximately harmonic h-convex functions depending on a given function

Awan¹,

Noor

Mihai

et al. 2019

Filomat

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“…Finally, combining relation (18) and inequality (19), we obtain , w, c). (20) Taking i � 3 in (28) and starting from the definition, we have…”

Section: Resultsmentioning

confidence: 96%

“…In a similar fashion, harmonic h-convexity unifies the various types of harmonic convexities. Definition 2 (see [19]). Consider a nonnegative function h:…”

Section: Introductionmentioning

confidence: 99%

Properties and Bounds of Jensen-Type Functionals via Harmonic Convex Functions

Mughal

Almusawa

Haq

et al. 2021

Journal of Mathematics

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Dragomir introduced the Jensen-type inequality for harmonic convex functions (HCF) and Baloch et al. studied its different variants, such as Jensen-type inequality for harmonic h -convex functions. In this paper, we aim to establish the functional form of inequalities presented by Baloch et al. and prove the superadditivity and monotonicity properties of these functionals. Furthermore, we derive the bound for these functionals under certain conditions. Furthermore, we define more generalized functionals involving monotonic nondecreasing concave function as well as evince superadditivity and monotonicity properties of these generalized functionals.

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“…As the above inequalities are very popular in estimating errors of quadrature rules, many researchers have massively studied them, as well as similar inequalities; one can consult, for example, [21][22][23][24][25][26][27][28][29][30] and references therein.…”

Section: Definition 1 ([1]mentioning

confidence: 99%