A generalization of Szász–Mirakyan operators based on q -integers
- 作者：Ali Aral
- 关键词：none ; color ; black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0V-4P61N60-B&_mathId=mml10&_user=1067359&_cdi=5656&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=58309ea5cbddf8b80287979f2cce1a01" t
- 刊名：Mathematical and Computer Modelling
- 出版年：2008
- 期刊代码：86_08957177
- 类别：cp
- 出版时间：May 2008
- 卷：47
- 期：9-10
- 页码：1052-1062
- 文件大小：272 K
摘要
In this paper, we introduce a generalization of Szász–Mirakyan operators based on ve&_udi=B6V0V-4P61N60-B&_mathId=mml2&_user=1067359&_cdi=5656&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=06fc164a4c7b5b5ccc86497d4c68a737" title="Click to view the MathML source" alt="Click to view the MathML source">q-integers, that we call ve&_udi=B6V0V-4P61N60-B&_mathId=mml3&_user=1067359&_cdi=5656&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=ea556cb4bceec89ea2c4cef42c087143" title="Click to view the MathML source" alt="Click to view the MathML source">q-Szász–Mirakyan operators. Depending on the selection of ve&_udi=B6V0V-4P61N60-B&_mathId=mml4&_user=1067359&_cdi=5656&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=ca16d301cfd26cae1d908e609a12166e" title="Click to view the MathML source" alt="Click to view the MathML source">q, these operators are more flexible than the classical Szász–Mirakyan operators while retaining their approximation properties. For these operators, we give a Voronovskaya-type theorem related to ve&_udi=B6V0V-4P61N60-B&_mathId=mml5&_user=1067359&_cdi=5656&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=11d860100d020e72fb186bc82852b348" title="Click to view the MathML source" alt="Click to view the MathML source">q-derivatives. Furthermore, we obtain convergence properties for functions belonging to particular subspaces of ve&_udi=B6V0V-4P61N60-B&_mathId=mml6&_user=1067359&_cdi=5656&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=630a640b53594da304b9ec6d1b20217b" title="Click to view the MathML source" alt="Click to view the MathML source">C[0,∞) and give some representation formulas of ve&_udi=B6V0V-4P61N60-B&_mathId=mml7&_user=1067359&_cdi=5656&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=20e684584936ea0963839dca9f0624e0" title="Click to view the MathML source" alt="Click to view the MathML source">q-Szász–Mirakyan operators and their ve&_udi=B6V0V-4P61N60-B&_mathId=mml8&_user=1067359&_cdi=5656&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=46a351d780aa81010a67249bff034e83" title="Click to view the MathML source" alt="Click to view the MathML source">rth ve&_udi=B6V0V-4P61N60-B&_mathId=mml9&_user=1067359&_cdi=5656&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=d06989e18dddd45f789df950651022af" title="Click to view the MathML source" alt="Click to view the MathML source">q-derivatives.