2019
DOI: 10.1186/s13660-019-2053-3
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( p , q ) $(p,q)$ -gamma operators which preserve x 2 $x^{2}$

Abstract: In this paper, we introduce (p, q)-gamma operators which preserve x 2 , we estimate the moments of these operators, and establish direct and local approximation theorems of these operators. Then two approximation theorems about Lipschitz functions are obtained. The estimates on the rate of convergence and some weighted approximation theorems of the operators are also obtained. Furthermore, the Voronovskaja-type asymptotic formula is also presented.

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Cited by 101 publications
(143 citation statements)
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“…For example, these tools may identify new biomarkers in urine or other samples to effectively diagnose bladder cancer earlier and further define subtypes for study. A recent publication shows a pattern of 14 metabolites, including lactic acid, leucine, valine, phenylalanine, glutamate, histidine, aspartic acid, tyrosine, serine, uracil, hypoxanthine, carnitine, pyruvic acid, and citric acid linked to early bladder carcinogenesis . Furthermore, metabolomics has been used to study how growing conditions, such as light exposure, can ultimately change the nutritional and phytochemical value, and ultimately the cancer fighting abilities, of broccoli sprouts .…”
Section: Future Approachesmentioning
confidence: 99%
“…For example, these tools may identify new biomarkers in urine or other samples to effectively diagnose bladder cancer earlier and further define subtypes for study. A recent publication shows a pattern of 14 metabolites, including lactic acid, leucine, valine, phenylalanine, glutamate, histidine, aspartic acid, tyrosine, serine, uracil, hypoxanthine, carnitine, pyruvic acid, and citric acid linked to early bladder carcinogenesis . Furthermore, metabolomics has been used to study how growing conditions, such as light exposure, can ultimately change the nutritional and phytochemical value, and ultimately the cancer fighting abilities, of broccoli sprouts .…”
Section: Future Approachesmentioning
confidence: 99%
“…We call it "model-wise" because the decoder takes the "model-wise" output of the encoder model as the single input for decoding. Such structure has been widely used for segmentation tasks [4]. Model-wise decoders focus more on the semantic context and may have trouble with segmenting fine details.…”
Section: Related Workmentioning
confidence: 99%
“…(1) Linear structure: The idea of this structure is to chain convolutions and pooling operations for feature extraction, such as in [4].…”
Section: Related Workmentioning
confidence: 99%
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“…In this Letter, we consider a computational model which originates from DFT for block copolymers [17] and has been extensively used to study morphological phases of diblock copolymers both analytically [15,16,[18][19][20][21][22][23][24] and numerically [13,[25][26][27]. Considerably less theoretical work exists for triblock copolymers.…”
mentioning
confidence: 99%