Several integral inequalities for (&lt;i&gt;α&lt;/i&gt;, &lt;i&gt;s&lt;/i&gt;,&lt;i&gt;m&lt;/i&gt;)-convex functions

Özdemi̇r, M. Emi̇n; Butt, Saad Ihsan; Bayraktar, Bahtiyar; Nasir, Jamshed

doi:10.3934/math.2020253

Cited by 11 publications

(8 citation statements)

References 12 publications

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“…For more recent integral inequalities for the class of s-convex functions and its generalizations via di¤erent integral opertaors, one can consult [11,17,20,21,28,30,34].…”

Section: Introductionmentioning

confidence: 99%

Quantum Hermite-Hadamard and quantum Ostrowski type inequalities for s-convex functions with applications

Ali,

BUDAK,

Ntouyas

et al. 2024

Preprint

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“…For more recent integral inequalities for the class of s-convex functions and its generalizations via di¤erent integral opertaors, one can consult [11,17,20,21,28,30,34].…”

Section: Introductionmentioning

confidence: 99%

Quantum Hermite-Hadamard and quantum Ostrowski type inequalities for s-convex functions with applications

Ali,

BUDAK,

Ntouyas

et al. 2024

Preprint

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show abstract

“…In this way, it is possible to think of the hypothesis of inequality as a separate area of mathematical analysis. For the literature regarding inequalities, see the references [1,7,9,17,19,20,28,30,31].…”

Section: Introductionmentioning

confidence: 99%

Some new notions of fractional Hermite-Hadamard type inequalities involving applications to the physical sciences

Ahmad,

Khokhar,

Suleman

et al. 2023

J. Math. Computer Sci.

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The term convexity in the frame of fractional calculus is a well-established concept that has assembled significant attention in mathematics and various scientific disciplines for over a century. It offers valuable insights and results in diverse fields, along with practical applications due to its geometric interpretation. Moreover, convexity provides researchers with powerful tools and numerical methods for addressing extensive interconnected problems. In the realm of applied mathematics, convexity, particularly in relation to fractional analysis, finds extensive and remarkable applications. In this manuscript, we construct new fractional identities for differentiable preinvex functions to strengthen the recently assigned approach even more. Then utilizing these identities, some generalizations of the Hermite-Hadamard type inequality involving generalized preinvexities in the frame of fractional integral operator, namely Riemann-Liouville (R-L) fractional integrals are explored. Finally, we examined some applications to the q -digamma and Bessel functions via the established results. We used fundamental methods to arrive at our conclusions. We anticipate the techniques and approaches addressed by this study will further pique and spark the researcher's interest.

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“…Controlled/living radical polymerization (CLRP or CRP) or reversible deactivation radical polymerization (RDRP) [11] is a series of useful techniques for the synthesis of tailormade polymers with applications in many fields such as electronics, adhesives, coatings, pharmaceutics, chromatography, biomaterials, etc. [12][13][14][15][16][17][18][19][20][21] These experimental techniques can be conducted as homogenous or heterogeneous processes; for instance, in bulk, solution or dispersion, using organic, ionic liquids, or "green" solvents, such as supercritical carbon dioxide (scCO2). [22][23][24][25][26][27][28][29] The most studied CLRP systems include atom transfer radical polymerization (ATRP), [30] reversible addition-fragmentation chain transfer (RAFT) polymerization, [31][32][33] and nitroxide-mediated radical polymerization (NMRP), [34,35] although other CLRP techniques such as…”

Section: Introductionmentioning

confidence: 99%

“…The scheme of the general model, Equations (11)-(23), is shown in Table 4 and the definitions of the moments used in the model equations are listed in Table 5. In the general model, thermal self-initiation (dimer D), chain transfer to small molecule (M, solvent S, chain transfer agent, Cta) and reinitiation of small radicals (B • , M • , D • , S • , Cta • ) are also considered in Equations (12), (14), (15), and (19), respectively.…”

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confidence: 99%

Model Discrimination between RAFT Polymerization Models Using Sequential Bayesian Methodology

Masoumi

Duever

Penlidis

et al. 2018

Macro Theory & Simulations

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The use of sequential Bayesian methodology for model discrimination purposes in reversible addition‐fragmentation transfer (RAFT) polymerization is analyzed and discussed from a mathematical model discrimination point of view. The RAFT models are detailed nonlinear mechanistic models from the literature, where the debate is still ongoing about their validity. A sensitivity analysis is performed first on the simulated models in order to identify the most informative process (measured) outputs from the candidate models with respect to model discrimination. Next, sequential Bayesian Monte Carlo model discrimination (SBMCMD) methodology is applied to discriminate between the two rival models. The effectiveness of the SBMCMD procedure in discriminating between the two proposed models (both describing basic RAFT polymerization kinetic trends successfully) is explored further. Most informative experiments are designed and suggested based on the design of experiments step of the SBMCMD methodology. The methodology is capable of selecting the “real” model.

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Several integral inequalities for (<i>α</i>, <i>s</i>,<i>m</i>)-convex functions

Cited by 11 publications

References 12 publications

Quantum Hermite-Hadamard and quantum Ostrowski type inequalities for s-convex functions with applications

Quantum Hermite-Hadamard and quantum Ostrowski type inequalities for s-convex functions with applications

Some new notions of fractional Hermite-Hadamard type inequalities involving applications to the physical sciences

Model Discrimination between RAFT Polymerization Models Using Sequential Bayesian Methodology

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