Some companions of Fejér’s inequality for convex functions

Tseng, Kuei-Lin; Hwang, Shiow-Ru; Dragomir, Sever S

doi:10.1007/s13398-014-0206-2

Cited by 13 publications

(6 citation statements)

References 8 publications

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“…If ϕ is a GA-convex function, then we obtain H(0) ≤ H(τ), (30) for all τ ∈ [0, 1]. The inequality ( 30) is a known result for a GA-convex function proved in [49].…”

Section: Proof We Know That Ifmentioning

confidence: 74%

Properties of GA-h-Convex Functions in Connection to the Hermite–Hadamard–Fejér-Type Inequalities

Latif

2023

Mathematics

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In this study, the Hermite–Hadamard–Fejér inequalities for GA-h-convex are proved, and the results for particular classes of functions are highlighted. In addition, several generalizations of the Hermite–Hadamard inequalities are presented. Some features of functions H and F that are naturally linked to the Hermite–Hadamard–Fejér-type inequalities for GA-h-convex have also been discussed. Finally, we obtain applications of the results related to the p-logarithmic mean and the mean of order p.

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“…If ϕ is a GA-convex function, then we obtain H(0) ≤ H(τ), (30) for all τ ∈ [0, 1]. The inequality ( 30) is a known result for a GA-convex function proved in [49].…”

Section: Proof We Know That Ifmentioning

confidence: 74%

Properties of GA-h-Convex Functions in Connection to the Hermite–Hadamard–Fejér-Type Inequalities

Latif

2023

Mathematics

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“…In [24], Tseng et al established Hermite-Hadamard and Fejér-type inequalities by using the mapping I. Furthermore, Fejér-type inequalities have also been proven by Tseng et al in [25] by using the mapping I. Hwang et al [25] obtained some Fejér-type inequalities in connection to the mappings G, H, I, Z κ .…”

Section: Introductionmentioning

confidence: 97%

Some Companions of Fejér-Type Inequalities for Harmonically Convex Functions

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2022

Symmetry

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In this paper, we present some mappings defined over 0,1 related to the Fejér-type inequalities that have been established for harmonically convex functions. As a consequence, we obtain companions of Fejér-type inequalities for harmonically convex functions by using these mappings. Properties of these mappings are discussed, and consequently, we obtain refinement inequalities of some known results.

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“…see [2,3,4,6,10,11,12,13,14,15,16,17] and the references therein. A modification for convex functions, which are also known as co-ordinated convex functions, was introduced by Dragomir in [4] (see also [2]) as follows: A function f : ∆ → R is said to be convex on the co-ordinates on ∆ if the partial mappings…”

Section: Introductionmentioning

confidence: 99%