Schur m-power convexity of generalized Hamy symmetric function

Wang, Wen; Shi-guo, Yang

doi:10.7153/jmi-08-48

Cited by 5 publications

(5 citation statements)

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“…There have been some papers written on this topic; for instance, Yang [39][40][41] discussed the Schur m-power convexity of Stolarsky means, Gini means, and Daróczy means, respectively. Wang and Yang [42,43] studied the Schur m-power convexity of generalized Hamy symmetric function and some other symmetric functions. Wang, Fu, and Shi [44], Yin, Shi, and Qi [45], and Kumar and Nagaraja [46] investigated the Schur mpower convexity for some special mean of two variables.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Schur m-power convexity of generalized geometric Bonferroni mean involving three parameters

Chu

2019

J Inequal Appl

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Schur m-power convexity of generalized geometric Bonferroni mean involving three parameters

Chu

2019

J Inequal Appl

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“…Then sgn (( 1 − 2 )/ ( 1 − 2 )) = 1, (i.e., ( ; 1 , 2 ) > 0.) Remark 12 (see [10]). By Lemma 11, we see that…”

Section: Definitions and Lemmasmentioning

confidence: 99%

“…The following lemma is clearly due to the monotonicity property of the function on R ++ . Lemma 11 (see [10]). For 1 , 2 > 0 with 1 ̸ = 2 , let be defined by…”

Section: Definitions and Lemmasmentioning

confidence: 99%

Schurm-Power Convexity of a Class of Multiplicatively Convex Functions and Applications

Wang

Shi-guo

2014

Abstract and Applied Analysis

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We investigate the conditions under which the symmetric functions , (x, ) = ∏ 1≤ 1 < 2 <⋅⋅⋅< ≤ ((∑ =1 ) 1/ ) , = 1, 2, . . . , , are Schur -power convex for ∈ R ++ and > 0. As a consequence, we prove that these functions are Schur geometrically convex and Schur harmonically convex, which generalizes some known results. By applying the theory of majorization, several inequalities involving the th power mean and the arithmetic, the geometric, or the harmonic means are presented.Rovent,a proved that (4) is a Schur convex function on .) They proved that * (x) is Schur convex, Schur geometrically and harmonically convex on . Recently, Yang [7-9] generalized the notion of Schur convexity to Schur m-power convexity, which contains the Schur convexity, Schur geometrical convexity, and Schur harmonic convexity. Moreover, he discussed Schur m-power convexity of Stolarsky means [7], Gini means [8], and Daróczy means [9]. Wang and Yang showed that generalized Hamy symmetric function [10] and a class of symmetric functions [11] are Schur m-power convex. Now we define the more general dual form of symmetric function.

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“…The linkers of the compounds in Figure S1 and Figure S2 include the ether, alkene, and the amide moieties. Among these, the amide linker is a privileged linker given its druglike properties. , The amide linker was first disclosed by Incyte and later on adopted by several other groups and companies (Figure S1 and Figure S2).…”

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“…In the NFAT assay, the compounds had an EC 50 (half-maximal effective concentration) below 1000 nM, with 79% of the compounds having an EC 50 cutoff below 300 nM (Table ). Such data are not found in publications. − The PD-1/PD-L1 inhibitors with an EC 50 above this cutoff are not considered potent enough to stimulate T cells to clinically relevant anticancer activity. Our most potent compound, 2 , features exceptionally high target affinity and demonstrated potency in cell-based assays with an EC 50 of 21.8 nM.…”

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confidence: 99%

Nonsymmetrically Substituted 1,1′-Biphenyl-Based Small Molecule Inhibitors of the PD-1/PD-L1 Interaction

Hec-Gałązka,

Tyrcha,

Barczyński

et al. 2024

ACS Med. Chem. Lett.

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Therapeutic antibodies directed against either programmed cell death-1 protein (PD-1) or its ligand PD-L1 have demonstrated efficacy in the treatment of various cancers. In contrast with antibodies, small molecules have the potential for increased tissue penetration; better pharmacology; and therefore, improved antitumor activity. A series of nonsymmetric C2 inhibitors were synthesized and evaluated for PD-1/PD-L1 interaction inhibition. These compounds induced PD-L1 dimerization and effectively blocked PD-L1/PD-1 interaction in a homogeneous time-resolved fluorescence (HTRF) assay with most inhibitors exhibiting IC50 values in the single-digit nM range and below. Their high inhibitory potency was also demonstrated in a cell-based coculture PD-1 signaling assay where 2 exhibited an EC50 inhibitory activity of 21.8 nM, which approached that of the PD-L1 antibody durvalumab (EC50 = 0.3–1.8 nM). Structural insight into how these inhibitors interact with PD-L1 was gained by using NMR and X-ray cocrystal structure studies. These data support further preclinical evaluation of these compounds as antibody alternatives.

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Schur m-power convexity of generalized Hamy symmetric function

Abstract: Abstract. In this paper, we investigate the Schur m-power convexity of the generalized hamy symmetric function1 r for x ∈ R n + and r ∈ N with 1 r n , which generalizes some known results.Mathematics subject classification (2010): 05E05, 26B25.

Cited by 5 publications

References 20 publications

Schur m-power convexity of generalized geometric Bonferroni mean involving three parameters

Schur m-power convexity of generalized geometric Bonferroni mean involving three parameters

Schurm-Power Convexity of a Class of Multiplicatively Convex Functions and Applications

Nonsymmetrically Substituted 1,1′-Biphenyl-Based Small Molecule Inhibitors of the PD-1/PD-L1 Interaction

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