2017
DOI: 10.1186/s13660-017-1413-0
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A basic problem of ( p , q ) $(p,q)$ -Bernstein-type operators

Abstract: In this note, we give an elaboration of a basic problem on convergence theorem of -analogue of Bernstein-type operators. By some classical analysis techniques, we derive an exact class of -integer satisfying with and under . Our results provide an erratum to corresponding results on -analogue of Bernstein-type operators that appeared in recent literature.

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Cited by 13 publications
(9 citation statements)
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“…POMs have been used as catalysts in organic reactions such as the nitration of phenols and the acetylation of alcohols and phenols. [13] For instance, [(C 4 H 9 ) 4 N] 5 [PW 11 CuO 39 (H 2 O)] was used as a POM catalyst for the liquid-phase oxidation of benzene to phenol and 9.2% benzene conversion and 91.8% selectivity to phenol was reported. [31] Because of reversible electrochemistry, light weight and polymeric nature, multi-electron reactions, and stability in the wide range of pH values and temperatures, POMs are good options as stationary storage materials. )…”
Section: Non-photocatalytic Applications Of Pomsmentioning
confidence: 99%
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“…POMs have been used as catalysts in organic reactions such as the nitration of phenols and the acetylation of alcohols and phenols. [13] For instance, [(C 4 H 9 ) 4 N] 5 [PW 11 CuO 39 (H 2 O)] was used as a POM catalyst for the liquid-phase oxidation of benzene to phenol and 9.2% benzene conversion and 91.8% selectivity to phenol was reported. [31] Because of reversible electrochemistry, light weight and polymeric nature, multi-electron reactions, and stability in the wide range of pH values and temperatures, POMs are good options as stationary storage materials. )…”
Section: Non-photocatalytic Applications Of Pomsmentioning
confidence: 99%
“…The energy levels of conduction and valence bands of POMs and g-C 3 N 4 were considered an effective factor in the improved photocatalytic performance. [56] Iron-containing POM (Fe III LysSiW) was synthesized with a chemical formula of [Fe(H 2 O) 5 4À hetero-polyanion and lysine moiety. The prepared composite showed good performance in 4-chlorophenol degradation by H 2 O 2 in both dark and irradiated systems.…”
Section: Application Of Poms and Their Composites In The Degradation mentioning
confidence: 99%
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“…A variety of different supports (including zeolites, mesoporous materials, metal oxides and fl uorides) were applied for Sonogashira couplings by Djakovitch and coworkers; however, the available substrate range was limited to aryl iodides and bromides in this case [195 -197] . Cai and coworkers reported reactions of aryl iodides at room temperature in the presence of an MCM -41 -supported Pd catalyst [198] . Application of ligand -free Pd/C in the Sonogashira reaction of aryl iodides was reported by Heidenreich et al [158] , Kotschy and coworkers [199] and Zhang [200] .…”
Section: Supported Palladium Catalysts In Other Coupling Reactionsmentioning
confidence: 99%
“…The plant alkaloid nicotine is an amine composed of pyridine and pyrrolidine rings (heterocyclic amines). It is a pharmacologically active substance found in tobacco [2][3][4]. Metabolism of nicotine in human beings yields cotinine as the major product.…”
Section: Introductionmentioning
confidence: 99%