2017
DOI: 10.1186/s13660-017-1586-6
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k-fractional integral trapezium-like inequalities through ( h , m ) $(h,m)$ -convex and ( α , m ) $(\alpha,m)$ -convex mappings

Abstract: In this paper, a new general identity for differentiable mappings via k-fractional integrals is derived. By using the concept of -convexity, -convexity and the obtained equation, some new trapezium-like integral inequalities are established. The results presented provide extensions of those given in earlier works.

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Cited by 80 publications
(84 citation statements)
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“…The solvents involved in organosolv pretreatment and nonenzymatic processes were also used as solvents for the depolymerization and upgrading of isolated or native lignin. [4,[192][193][194] Xu et al recently reviewed lignin conversion strategies [195] and showedt hat many studies give rise to high-yield conversion of lignin model compounds into lignin monomers in the aqueous phase using acid/alkali hydrolysis and hydrogenolysis. However,t he authorsa lso showt hat these strategies did not perform well in the depolymerization of real lignin.…”
Section: Solvent Effects On Lignin Solubilitymentioning
confidence: 99%
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“…The solvents involved in organosolv pretreatment and nonenzymatic processes were also used as solvents for the depolymerization and upgrading of isolated or native lignin. [4,[192][193][194] Xu et al recently reviewed lignin conversion strategies [195] and showedt hat many studies give rise to high-yield conversion of lignin model compounds into lignin monomers in the aqueous phase using acid/alkali hydrolysis and hydrogenolysis. However,t he authorsa lso showt hat these strategies did not perform well in the depolymerization of real lignin.…”
Section: Solvent Effects On Lignin Solubilitymentioning
confidence: 99%
“…[127] Am ajor reasonf or this difference is that both native lignin and the catalysta re in the solidp hase,w hich limits the mass transfer between the lignin reactanta nd the active sites of the heterogeneous catalyst. [194] Therefore, the use of ah omogeneous liquid solution of lignin [4,[192][193][194] and/or ah omogeneous catalyst [195,196] was shown to further favor lignin depolymerization. Organosolv lignins, which can be dissolved by solvents such as acetone, ethanol, methanol,a nd THF,a re relatively attractive substrates for upgrading.…”
Section: Solvent Effects On Lignin Solubilitymentioning
confidence: 99%
“…[6]. The height of GaN columns increases with increased silane flow, because a high silane flow changes growth processes on the surface and it passivates the sidewalls of GaN columns with a Si-rich layer [6,7]. Several groups report on the effects of surface passivation on the performance of GaN devices [8][9][10].…”
mentioning
confidence: 99%
“…As the flagship, titanium dioxide (TiO 2 ) semiconductors show many prominent advantages including low cost, high thermal/ chemical stability, and strong oxidizing ability. [1][2][3] These features favor the applications of TiO 2 nanomaterials as an excellent photocatalyst for degradation of organic pollutants, especially in wastewater treatment. [4] Unfortunately, the relatively poor charge transport ability and wide bandgap (~3.2 eV) of TiO 2 go against the light absorption and accelerate the recombination between electrons and hole pairs, leading to the low catalytic activities.…”
Section: Introductionmentioning
confidence: 99%